"If we’re to leave with a deal, we need the EU to jump over from its side and join us there, showing its own willingness to do a deal that the UK parliament can support," he said.
Senior EU officials have rejected Johnson's proposals and urged him to provide several clarifications, with arrangements for the post-Brexit Irish border still the main sticking point.
Johnson said British voters "want to move on" from Brexit.
"So I say to our European friends: grasp the opportunity that our new proposal provides," he added, urging Brussels to join London "at the negotiating table in a spirit of compromise and co-operation."
"We can do it with a deal if the EU is willing," Johnson said, insisting that Britain will leave the bloc, with or without a deal, on October 31.
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