The plan, outlined in a seven-page document, would see Northern Ireland stay in the European single market for goods, but leave the customs union - resulting in new customs checks.
The Northern Ireland Assembly would get to approve the arrangements first and vote every four years on keeping them.
The European Commission said there had been progress but "problems" remained.
Irish Prime Minister Leo Varadkar said the new blueprint did not "fully meet the agreed objectives of the backstop", in terms of upholding the EU's single market, protecting peace in Northern Ireland and supporting economic co-operation with the Republic of Ireland.
But he said he wanted an agreement and talks would continue.
The UK is set to leave the EU on 31 October and the government has insisted it will not negotiate a further delay beyond the Halloween deadline.
Speaking at the Conservative Party conference earlier on Wednesday, Boris Johnson said the only alternative to his Brexit plan was no-deal.
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