Video report by ITV News Correspondent Dan Rivers
The Government will "test to the limit" a new law designed to block a no-deal Brexit if an agreement with the EU is not reached by October 19.
Foreign Secretary Dominic Raab said the government would abide by the law but would "look very carefully" at its "interpretation" of the legislation.
A new law, which should gain royal assent on Monday, aims to stop a no-deal exit from the European Union on October 31, if an agreement cannot be reached with the EU by the European Council meeting on October 17 and 18.
The law, which was rushed through Parliament last week, will force the Prime Minister to ask the EU for a three-month deadline extension if no agreement is in place by October 19.
However, on Sunday, French Foreign Minister Jean-Yves Le Drian said his country would veto any extension request due to a "worrying lack of progress" towards a Brexit deal, and a lack of realistic proposals as an alternative to the Irish backstop.
ITV News Political Correspondent Romilly Weeks said it was "unlikely" that France would carry out this threat, as they made similar "protestations" when Theresa May asked for the last extension.
Speaking on Sky News' Sophy Ridge On Sunday, Mr Raab said the Government remained committed to getting a deal.
However, on Saturday, Amber Rudd quit the Conservative Party and her post as work and pensions secretary, with one of her reasons being that not enough work is being done to leave the EU with a deal.
The Hastings and Rye MP said that despite repeatedly asking, she was only shown a "one-page summary" when asked for evidence of negotiations.
However, Prime Minister Boris Johnson has repeatedly said the UK will leave the EU on Halloween with or without a deal.
Last week, Mr Johnson added he would "rather be dead in a ditch" that ask the EU for a Brexit extension.
Mr Johnson was quoted in two Sunday newspapers saying he will “refuse to accept” any “pointless delay” on Brexit, in the clearest move yet that Downing Street is looking for ways to disobey a law blocking no-deal.
The Prime Minister also accused MPs of “trying to wreck” the negotiations and reiterated his commitment to taking Britain out of the EU by Halloween.
The Sunday Times reported that Boris Johnson wants a Supreme Court battle over whether he can defy the rebel law demanding a Brexit extension.
Should Mr Johnson break the law, he could be forced from office, impeached and even face jail.
However, speaking on Sunday, Mr Raab said the Government will "behave lawfully" and that the new law would be "challenged in the courts".
He continued: "But what we are going to do with that legislation is test very carefully what it does and doesn't require, and that's not only the lawful thing to do, I think it's the responsible thing to do."
Speaking on BBC One's The Andrew Marr Show, Chancellor Sajid Javid echoed his Cabinet colleague that "of course this Government will obey the law.
"We are going to continue to work towards exit on October 31.
"We will leave on October 31.
"We will work for a deal, we will keep putting all our effort into that and preparations for no-deal just in case that is the only way we can leave."
But he too said Mr Johnson "absolutely will not" ask for an extension in an October council meeting with the EU.
He continued: "We will not change our policy, we will have to wait and see.
"We will be consistent with obeying the law but also sticking to our policy, and you will have to wait and see what happens because there is a lot of days between now and October 19."
Meanwhile Labour attached the Government's position as "extraordinary".
Shadow attorney general and Labour peer Baroness Shami Chakrabarti told Sophy Ridge: "I think the position is irresponsible and elitist, the idea there's one law for Boris Johnson and his mates and another law for everyone else, it's appalling."
She added: "Every tinpot dictator on the planet throughout history has used the excuse of having the people on their side to break the law to shut down Parliament and all the rest of it, it's absolutely extraordinary and I think it's very un-British, as was the purge of the 21 MPs, who are Conservatives, they're not secret Corbynistas."
She went on: "The legislation is crystal clear, if you don't have a deal in the next few weeks you have to apply for the extension, it's a duty that's laid in the legislation on the Prime Minister personally...
"What I think is going on here is that Johnson and co, deliberately using breaking the law as a kind of dog whistle because they think it makes them look tough, but I just think it makes them look appalling, which is why I want this to be sorted out in Parliament, which is why shutting down Parliament and seeking to dissolve Parliament tomorrow, so that you can crash out is terrible."
Meanwhile, shadow chancellor John McDonnell said the country is is "in an extremely serious constitutional position.
"We don't believe that we can pin him [Boris Johnson] down and I don't trust him an inch, and I don't think anyone does.
"We've got a Prime Minister who has said he would not abide by the law.
"We're in a situation where no-one can trust while he's in place what could happen."
Meanwhile, Nigel Farage has told The Sunday Times he stands ready to offer a “non-aggression pact” to the PM that he predicted could win a 100-seat majority for the Tories and Brexit Party.
However, Mr Javid refused to rule out a pact with the Brexit Party in a general election, telling the BBC that the Conservative Party does not "need" electoral alliances.
The PM said he would give Labour “one last chance” to agree to an autumn general election on Monday but, if that was declined, the Government would “simply carry on” he vowed.
He is set to ask MPs to agree to a snap election when they return to the Commons after a similar move failed to secure the two-thirds majority required on Wednesday.
“We will surmount all the obstacles in our path,” continued Mr Johnson. “We will work tirelessly for a deal, even though Corbyn would like to make that task far harder.
“But whatever happens we will get ready to come out on October 31 and we will serve this country and its people with the energy and commitment they deserve.”