Prime Minister Boris Johnson said he made a "genuine effort to bridge the gap". To get a new Brexit deal with the EU.
He told MEPs that his plan to keep Northern Ireland in the European single market for goods but to leave the customs union was a "compromise".
But Jeremy Corbyn criticized the "unrealistic and harmful proposals".
Irish Prime Minister Leo Varadkar said the new plans were welcome, "but remained behind in a number of aspects".
But his Swedish counterpart Stefan Lofven said that despite "question marks" regarding the proposals, they represented a "good start to negotiations".
The European Commission stated that the British proposal contained "problematic points" and "further work is needed".
Focus Group in the European Parliament said the plan's "in its present form" did not constitute an agreement that MEPs could ratify.
"The suggestions do not address the real issues that need to be addressed if the backstop is to be removed," the group added.
Outgoing President of the European Council, Donald Tusk tweeted that the EU was "open but still unconvinced" about the plan and would "stand fully behind Ireland".
The UK Government is looking forward to a period of intense negotiations aimed at reaching a final agreement at an EU summit on 17 October.
The British Prime Minister has announced that he will leave or leave the EU on 31 October without a deal.
In the Commons, Mr. Johnson appealed to MPs to support his Brexit plan – a tone change that emerged from the stormy scene in Parliament last week, such as the BBC's political correspondent, Nick Eardley, emphasizing:
"This government has moved, our proposals are a compromise, and I hope that the House can now come together in the national interest behind this new agreement," Johnson said.
His proposal aims to replace the Irish "backstop" the limit in the existing readmission agreement – which was rejected by the deputies three times.
The Backstop is the controversial "insurance policy" intended to maintain a free-flowing border on the island of Ireland, criticized by critics. including PM anxiety could indefinitely include Britain in EU trade rules. It has proved to be the sticking point in the negotiations.
"I think this is our chance and your chance to make a deal," Mr Johnson told the MP. But he said the two sides were "a bit far from a resolution."
Mr. Johnson added that the plan would mean that no controls or infrastructure would be required at or near the border between Ireland and Northern Ireland.
But the Labor Party leader, Mr. Corbyn, said: "The current proposals would cover the entire British economy, especially the Northern Irish economy, would damage and undermine the Good Friday Agreement. "
He said the proposals" reject any form of customs union, something that is required of every economic and industrial organization in Britain and every union ".
"They want to drop EU standards." To the workers' rights, regulations and consumer standards and to a race to the bottom "he said Johnson" does not dig the reality of a functioning backstop. "
" It's a half-hearted plan by (prime minister adviser) Dominic Cummings and his Brexit fanatics, "Blackford even left the podium at the Tory conference."
What's in the plan?
According to Johnson's proposals, which he calls a "wide landing zone" for a new agreement with the EU:
- Northern Ireland would leave the EU Customs Union in early 2021 along with the rest of the UK
- But Northern Ireland would consent Politicians in the Northern Ireland Assembly continue to apply EU legislation on agricultural and other products – what he calls an "All-Island Regulatory Zone"
- This scheme could theoretically continue indefinitely, but the approval of the Northern Irish politicians would have to be overtaken every four years.
- Customs controls for goods traded between the UK and the EU would be "decentralized", with paperwork electronically and only a "very small number" of physical checks
- These controls should be outside the border, in business premises or at "elsewhere in the supply chain".
The government also promises a "New Deal for Northern Ireland" with financial commitments to address the changes.
Lib Dem leader Jo Swinson said there was "real fear" of his proposals on the Northern Ireland border
She said his plan was "denounced as the worst of both worlds" and asked, "Will the Prime Minister go to the Northern Ireland border now and listen to the people and communities there, or does he care? "
The Conservative MPs, however, have expressed their support for the proposals.
Brexiter Sir Bill Cash welcomed the plan and the" indications "of the progress of these negotiations."
Steven Crabb, MP of Tory, praised Johnson for the "serious intent and effort he is undertaking," saying he "proves many of his doubters wrong."
He said the "constructive tone" of "Mr. Johnson" stands in stark contrast to the opposition parties [who] who continue to put their faces against their own voters. "
However, the proposals require EU approval to progress.