Boris Johnson has written to European Council President Donald Tusk outlining his demands in a bid to re-launch negotiations over Brexit.
The Prime Minister proposed replacing the Irish backstop with a commitment to put in place alternative arrangements by the end of a post-Brexit transition period.
Johnson calls for the backstop - an insurance policy to avoid the return of a hard border on the island of Ireland - to be removed from the deal the EU reached with his predecessor Theresa May.
He said that he believed it was possible to reach an agreement and that doing so was his government's "highest priority".
However he also repeated his promise to take Britain out of the EU on October 31 with or without a deal if necessary.
Johnson wrote: "The UK and the EU have already agreed that 'alternative arrangements' can be part of the solution.
"Accordingly: I propose that the backstop should be replaced with a commitment to put in place such arrangements as far as possible before the end of the transition period, as part of the future relationship."
The PM added that Britain was ready to look "constructively and flexibly" at what commitments could help provide confidence about what would happen if such arrangements were not fully in place at the end of that period.
The backstop would force Britain to obey some EU rules if no other way could be found to keep the land border open between Northern Ireland and EU member Ireland. Dublin says this is crucial to maintaining peace on the island.
In his letter to Tusk, Johnson said the backstop was "simply unviable" because it is "anti-democractic and inconsistent with the sovereignty of the UK as a state" but that he was committed to ensuring there was no return to a hard border.
He continued: "The government will not put in place infrastructure, checks, or controls at the border between Northern Ireland and Ireland. We would be happy to accept a legally binding commitment to this effect and hope that the EU would do likeswise."
The EU has so far said the withdrawal deal cannot be renegotiated. Johnson is due to carry out his first foreign trip as prime minister this week to meet with German Chancellor Angela Merkel and French President Emmanuel Macron.
Johnson added: "Time is short. But the UK is ready to move quickly, and, given the degree of common ground already, I hope that the EU will be ready to do likewise."
