The Tory leader faces a struggle to secure backing for the proposals, which have drawn criticism in the Commons and from the EU.
Boris Johnson has launched a charm offensive aimed at rallying support for his Brexit plan at Westminster and with EU leaders.
Striking a notably conciliatory tone following recent angry exchanges, the prime minister told MPs he had made a “genuine attempt to bridge the chasm” with Brussels by making compromises and secure a fresh divorce deal.
While the proposals were not all that he wished for, he insisted they were better than to “remain a prisoner” of the current Brexit deadlock.
But he faces a struggle to secure backing for the proposals, which have already drawn criticism both in the Commons and from the EU.
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Jeremy Corbyn said no Labour MP could support the “reckless deal” that he said would threaten the Good Friday Agreement, which secured peace in Northern Ireland.
The Irish government has also raised objections to the post-Brexit arrangements proposed in Mr Johnson’s plan, including customs checks on the island.
The European Parliament’s Brexit Steering Group (BSG) has “grave concerns” about Boris Johnson’s proposals, which it said cannot be backed “in their current form”.
Mr Johnson is now engaged in a frantic round of diplomatic negotiations aimed at hammering out a deal in time for the crunch EU summit on 17 October.
It comes after he unveiled a plan to address the thorny issue of the Irish backstop.
The controversial insurance policy aimed at avoiding a hard border between Northern Ireland and the Republic saw Theresa Mays deal rejected three times by MPs.
The alternative nw proposed by the PM would keep Northern Ireland tied to single market rules for trade in goods while leaving the customs union with the rest of the UK.
In a plea to MPs to “come together in the national interest behind this new deal”, Mr Johnson told the Commons: “This Government’s objective has always been to leave with a deal and these constructive and reasonable proposals show our seriousness of purpose
“They do not deliver everything that we would’ve wished, they do represent a compromise, but to remain a prisoner of existing positions is to become a cause of deadlock rather than breakthrough.
“So we have made a genuine attempt to bridge the chasm, to reconcile the apparently irreconcilable and to go the extra mile as time runs short.”
Labour leader Mr Corbyn told the Commons: “No Labour MP could support such a reckless deal that will be used as a springboard to attack rights and standards in this country.”
However, Mr Johnson appeared to have won over support from the DUP, Eurosceptics within his own party and some opposition MPs wishing to avoid a no-deal.
But this could change if he is forced to make further compromises by Brussels.
Irish prime minister Leo Varadkar has said Boris Johnson’s Brexit plans “fall short in a number of aspects”.
On a visit to Sweden, Mr Varadkar said he could not fully understand how the UK saw Northern Ireland and the Repblic operating under different customs regimes without the need for customs posts.
On the issue of the proposed Stormont veto on new regulatory arrangements, Mr Varadkar also said no one party should be able to block the majority view on the island.
“Any consent mechanism and democracy mechanism must reflect the views of the majority of people in Ireland and Northern Ireland,” he said.
Meanwhile, European Commission spokeswoman Natasha Bertaud told reporters that “we have many questions on the text” of the Brexit proposal that “need to be answered by the UK and not the other way around”.
Under the plan, the arrangements would start in 2021 at the end of the proposed transition period unless there was a long-term trade agreement in place and would continue until one was reached.
An explanatory note from the UK government said a system of declarations for goods traded between the North and the Republic meant only a “very small proportion” would be subject to physical customs checks.
When they were necessary, it said that they would take place well away from the border, at the traders’ premises or other designated locations.
Labour MP Hilary Benn, who heads the Commons Brexit select committee said the PM had announced that “there will be customs checks in Northern Ireland” and risked “the return to a hard border”.
Mr Johnson insisted he was “mistaken if he believes that it will involve – any of our proposals – and necessitate any kind of checks at the border”.
The PM said: “That is absolutely untrue or indeed any kind of hard border because that is – I must him respectfully, tell him respectfully – that is untrue.”