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”.
Irish PM Leo Varadkar said the new plans were welcome, but “fall short in a number of aspects”.
Outgoing European Council President Donald Tusk tweeted the EU was “open but still unconvinced” about the plan, and would “stand fully behind Ireland”.
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The European Commission said there were “problematic points” in the UK’s proposal and “further work is needed”.
And the main Brexit-focused group at the European Parliament said the plans “in their current form” did not represent a deal MEPs could ratify.
“The proposals do not address the real issues that need to be resolved if the backstop were to be removed,” the group added.
But Swedish Prime Minister Stefan Lofven said that, despite “question marks” over the proposals, they represented a “good start for negotiations”.
The EU’s chief Brexit negotiator, Michel Barnier, has said he will be in a better position to judge possible future negotiations with the UK once he has spoken to his UK counterpart, David Frost.
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 – a change in tone seen from the stormy scene in Parliament last week, as BBC political correspondent Nick Eardley pointed out: