Prime Minister Boris Johnson says 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”.
But his Swedish counterpart Stefan Lofven said that, despite “question marks” over the proposals, they represented a “good start for negotiations”.
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.