Boris Johnson has claimed the UK could get through a no-deal Brexit, but said that outcome would represent a "failure of statecraft" by all concerned.
The Prime Minister, in Dublin for talks with Irish Prime Minister Leo Varadkar, said he believed it was possible to get a new Brexit agreement by October 18.
Speaking in Ireland, Mr Johnson insisted he wanted "to find a deal."
He continued: "I have looked carefully at no-deal.
"Yes, we could do it, the UK could certainly get through it, but be in no doubt that outcome would be a failure of statecraft for which we would all be responsible," he said.
Mr Johnson has previously said he can only agree to a deal if the backstop is removed, but Mr Varadkar told him "in the absence of agreed alternative arrangements, no backstop is no-deal for us".
Following the meeting, a British-Irish joint statement was released, which said the two leaders had a constructive meeting and "common ground was established" but "significant gaps remain".
In the press conference Mr Varadkar said that while Ireland was open to alternative solutions to the Northern Ireland backstop, they had yet to see any "legally workable" proposals from the UK.
When asked by ITV News Political Correspondent Carl Dinnen if he had any ideas to solve the backstop, the PM said: "There are an abundance of proposals that we have but I don't think reasonable to share with you today Carl, we have indicated areas progress needs to be made."
"Be in no doubt we can do it and will address it enthusiastically.
"30 years - I mean 30 days ought to be enough if we concentrate our minds."
Meanwhile, Downing Street confirmed that Parliament will be prorogued at the end of business on Monday, after a vote on an early general election has been held.
Opposition leaders meeting in Westminster confirmed they would block the Prime Minister's latest attempt to force a general election in a vote later in the day.
They instead agreed that when Parliament returns following prorogation, they will vote down the Queen's Speech and trigger a general election.
Labour leader Mr Corbyn said: "We will take every parliamentary action we can and continue the public campaign to get no-deal taken off the table.
"And then let's have a general election and see what kind of Government the people of this country want."
A party spokeswoman said: "All leaders agreed that they would not support Boris Johnson's ploy to deny the people their decision by crashing us out of the EU with no deal during a general election campaign."
Responding to the government's apparent refusal to request a Brexit extension, Mr Corbyn said: "It is extraordinary that we have a prime minister who has lost every vote he has put to Parliament in the few days it has been back that now goes around the country saying that he is now going to defy parliament.
"Democracy requires that elected governments are responsible to Parliament itself."
At the cross-party meeting, Plaid Cymru Westminster leader Liz Saville Roberts told opposition leaders they must be ready to impeach the PM if he refuses to ask the EU for an Article 50 extension.
After the meeting, she said: "I am glad that as opposition parties, we are united in our belief that Boris Johnson's attempt to undermine the rule of law must be stopped.
"If the Prime Minister refuses to seek an extension to the period under Article 50, he will have broken the law - plain and simple - and he must be subject to legal repercussions.
"I told other opposition parties this morning that if he does break the law, we should be ready to impeach Boris Johnson - a procedure that he himself supported in 2004 when current Plaid Cymru leader Adam Price sought to impeach Tony Blair for lying."
A former government special advisor told ITV News that "an election is absolutely inevitable at this stage," even if MPs vote against one tonight.
Jason Stein, who was Amber Rudd's special advisor before she resigned, said: "The government doesn't currently have the numbers for the election, what is has is a clear purpose and strategy that is currently outwitting the rebels who do have the numbers."
He claimed the government has mechanisms to force through an election, "either through the courts forcing an extension on them, or through the prime minister resigning".
If MPs vote for an election before that date, then the Speaker - who has been in his role for 10 years - says he will not stand.