Prime Minister Boris Johnson has said he has made a “genuine attempt to bridge the chasm” in order to get a fresh Brexit deal with the EU.
He told MPs his plan which would see Northern Ireland stay in the European single market for goods but leave the customs union were a “compromise”.
But Jeremy Corbyn criticised the “unrealistic and damaging proposals”.
And the European Commission said there were “problematic points” in the UK’s proposal and “further work is needed”.
Tanaiste Irish deputy Prime Minister Simon Coveney has said there will be no deal if the latest plan put forward by the UK is the “final proposal”.
The UK government hopes to begin a period of intense negotiations with the aim of reaching a final agreement at an EU summit on 17 October.
The prime minister has said the UK will leave the EU on 31 October, with or without a deal.
In the Commons, Mr Johnson appealed to MPs to support his Brexit plan and a change in tone seen from the stormy scene in Parliament last week. Report says.
“This government has moved, our proposals do represent a compromise and I hope that the House can now come together in the national interest, behind this new deal,” Mr Johnson said.
His proposal aims to replace the Irish border “backstop” in the existing withdrawal agreement which has been rejected three times by MPs.
The backstop is the controversial “insurance policy” that is meant to keep a free-flowing border on the island of Ireland but which critics – including the PM fear could trap the UK in EU trading rules indefinitely. It has proved to be the sticking point in negotiations.
“I believe this is our chance and their chance to get a deal,” Mr Johnson told MPs. But he said the two sides were “some way from a resolution”.
Mr Johnson added that the plan would mean there was no need for checks or infrastructure between Ireland and Northern Ireland.
But Labour leader Mr Corbyn said: “The current proposals would damage the whole UK economy, the Northern Irish economy especially and would undermine the Good Friday agreement.”
He said the proposals “reject any form of customs union, something demanded by every business and industry body in Britain and every trade union”.
“They want to ditch EU standards on workers’ rights, regulations and consumer standards and engage in a race to the bottom,” he said.
The SNP’s Westminster leader Ian Blackford said the PM will, “never have the consent of Scotland” for his Brexit deal, saying Mr Johnson “doesn’t grasp the reality of a workable backstop”.
“It is a half-baked plan from (the prime minister’s adviser) Dominic Cummings and his Brexit fanatics,” Mr Blackford said.
“The proposed deal is dead before it even left the podium of the Tory conference.”
The government is also promising a “New Deal for Northern Ireland”, with financial commitments to help manage the changes.
Lib Dem leader Jo Swinson said there was “genuine fear” about his proposals at the Northern Ireland border.
She said his plan “has been denounced as the worst of both worlds”, asking: “Will the prime minister now go to the Northern Ireland border and listen to the people and communities there or does he not care?”
However, Conservative MPs voiced their support for the proposals.
Brexiteer Sir Bill Cash welcomed the plan and the “indications of progress in these negotiations”.
Tory MP Steven Crabb commended Mr Johnson on the “serious intent and effort he is adopting”, saying he is “proving many of his doubters wrong”.
He said the “constructive tone” of Mr Johnson “stands in stark contrast to the opposition parties who continue to set their face against their own voters”.
But the proposals will need the agreement of the EU in order to progress.