Britain's post-Brexit security plans have been compared to a wish list to Santa, as Sajid Javid acknowledged the Theresa May's deal is not "perfect in every sense".
The comments came as MPs took part in the second of five days of debates on the Prime Minister's Brexit deal in the House of Commons.
MPs are set vote on whether to pass Mrs May's deal on December 11.
The Government has now also published the full legal advice it received on the Withdrawal Agreement from attorney general Geoffrey Cox.
Mrs May was forced into the move after MPs voted to find ministers in contempt of Parliament by withholding the information.
Home Secretary Sajid Javid opened the debate on Wednesday, with security one of the main topics.
The Home Secretary said he believed the Brexit agreement on offer is the "best option available" in ensuring a "smooth exit", although he came under fire from the DUP for suggesting it will allow the UK to "take back control of our borders" and end the jurisdiction of the European Court of Justice (ECJ) in the UK.
Mr Javid also recognised comprises have been made with Brussels but argued the deal was better than an "unplanned" no-deal Brexit, which he claimed would likely cause some disruption to security operations.
But as MPs questioned the level of crime and security cooperation between the UK and EU under the deal, Labour former Europe minister Chris Bryant said the Government's aims were "no more deliverable than a letter to Santa Claus".
Mr Javid also told MPs that it remains his intention to publish the Government's immigration white paper before the end of the year.
In response to a question from Labour's Yvette Cooper, he said: "I can tell her that it's certainly still my intention to publish it in December and that hasn't changed."
Mr Javid later said the agreement secured by Theresa May will allow the UK to continue to work with Brussels on cross-border investigations on modern slavery, using DNA databases to catch criminals, the fast-track extradition of suspects, along with working alongside Europol and Eurojust.
Mr Bryant, intervening, said: "That's a great wish list, and it's all in the Political Declaration, but it's no more deliverable than a letter to Santa Claus.
"It really isn't."
The MP for Rhondda added: "It's all very well having a wish list, but how on earth could a serious Member of Parliament vote for nothing more than a wish list?"
However, shadow foreign secretary Emily Thornberry, went one step further than the others, saying Mrs May's deal failed to protect UK citizens.
"The first duty of every Government is the duty to protect the safety and security of its citizens and the Prime Minister's deal fails," Ms Thornberry said.
"It is the very definition of making the British people, who our first duty it is to protect, less safe and less secure."
Foreign Office minister Sir Alan Duncan was scolded by Speaker John Bercow for repeatedly shouting "nonsense" and "what rot" at Ms Thornberry before Jeremy Hunt could respond on behalf of the Government.
The Foreign Secretary, concluding the second day of debate, said: "Under the Withdrawal Agreement our law enforcement agencies will continue to use EU tools and databases throughout the transition period and as the transition period concluded paragraph 87 states that we have agreed to continue to exchange information."
Earlier in the day, Mrs May's former defence secretary Sir Michael Fallon also attacked her Brexit deal, telling the Commons it is "a risk too far" and will not have his support without improvement.
But the Conservative MP for Sevenoaks added no deal was not acceptable and a second referendum would not work "not because it would be divisive but because it would not be decisive".
He said: "If we are to surrender our vote, our voice and our veto then we need to have a deal that's worth all the risks of not knowing how it's going to work out, and we do not have that at the moment.
"This so-called deal is a gamble - we put all our cards and all our money on the table and then wait for another two years for the EU to set the rules of the game and that is a risk too far."
Shadow home secretary Diane Abbot also likened Mrs May's deal to a "wish list", telling the Commons: "On the question of security, assertions, aspirations, a wish list is not enough, we need a treaty...
"At the worst, the gaps and loopholes created under this exit agreement could create a situation in which organised criminals and terrorists in the EU might come to regard the UK as a relative safe haven from justice."
Ongoing cooperation in cases and investigations "may ultimately be compromised", Ms Abbott said, adding: "On the basis of security concerns alone no member of this House should be signing off this deal."
Labour's Yvette Cooper, chairwoman of the Home Affairs Select Committee, called for a "security backstop" in the Brexit deal.
She said: "Perhaps the most troubling thing of all is there is no security backstop in this deal.
"Unlike for Northern Ireland, unlike for trade, there is no backstop to continue security cooperation until a future security treaty or overarching treaty is agreed, so if the transition period runs out, and we have not got these things agreed, we will lose these vital capabilities."
Meanwhile, former Tory minister Sam Gyimah, who resigned over the direction of Brexit negotiations, told the Commons that the second phase of negotiations had been "set up for failure".
He also said Mrs May's government had kicked into the long grass" all the big issues of Brexit.
"The deal has been described as having a Remain-flavour, even as a Remainer it became quite clear to me that this deal is not politically or practically deliverable, that it will make us poorer and also risk the union," Mr Gyimah told the commons.
He added: "The home secretary admitted it might not be perfect, almost implying this is like trying on a pair of shoes, not the right colour, maybe a little bit tight but you could get on with it and life would be fine.
"But actually this is like shoes that have holes in the soles. This deal is fatally flawed."
While some MPs attacked the Prime Minister's deal, some attacked Mrs May herself, calling for her to go if she could not get the sort of deal they wanted.
Conservative MP Zac Goldsmith suggested Theresa May may need to be replaced so the Brexit deal could be renegotiated.
He said: "I believe the Government is going to lose this vote next week, I hope - I'm afraid to say - the Government loses the vote next week.
"And then either this prime minister or, if she will not do it, another prime minister must take it back to the EU and change it."
However, not all MPs are against the Prime Minister's Brexit deal.
Tory former cabinet member Stephen Crabb said voting down the Prime Minister's deal "resolves nothing at all" and there was nothing simple, nothing straightforward about withdrawing the UK from the EU after 40 years.
He said: "The truth is we have a less than perfect Brexit deal in front of us because that was always going to be the case."
Turning to fellow Tories, he said the deal on the table is "already our deal, it's already got all of our names attached to it, because... the deal fundamentally has been shaped by decisions that we all took as a governing party".
He said: "We are responsible for the way that this deal has been shaped and so we will share in the responsibility for what happens next."
He added: "The reason that I'm voting for this imperfect deal, yes, it could have been better, it could have been so much better if we'd used our time much better as a Government and a party over the last two years, but I'm going to vote it through because I believe in doing Brexit in a responsible way that protects the interests of my constituents and abides by the outcome of the referendum 2016."
It was not just in the Commons that Mrs May's Brexit deal was attacked, in a three-day debate on the Withdrawal Agreement in the House of Lords the blueprint was lambasted by Tory peers.
Conservative former leader Lord Howard of Lympne likened Mrs May's plan to the surrender treaty of a defeated nation.
Lord Howard argued the UK would be unable to leave the controversial backstop without the EU's consent and warned that member states would use it to "exercise leverage" against the UK.
With MPs poised to vote on the deal next week, he said it achieved the opposite of taking back control and that the Government should recognise "this deal is dead".
He went on to urge the Government to intensify talks with Brussels on preparations for a no-deal, including temporary arrangements aimed at minimising disruption after Brexit day on March 29.
However, as in the Commons, Mrs May received support from some of the Lords.
Independent crossbencher Lord Butler of Brockwell, who headed the Civil Service for a decade, said: "The Withdrawal Agreement is neither better nor worse than I expected from the outset of the negotiations.
"I note that none of those in favour of our leaving the EU has proposed an alternative departure agreement which would have had any chance of acceptance by the EU, nor are they doing so now.
"If the United Kingdom is to leave the European Union, a departure agreement on the lines proposed by the Government and agreed with the EU is the inevitable consequence.
"It is much better than no deal.
"It is worse than the alternative of staying within the EU, but that is not the choice before us."