The German foreign minister also rejected British attempts at obtaining further concessions that can satisfy hardliners and critics of the deal in London.
I comes after British prime minister Theresa May's government last week rejected the backstop it had previously agreed and backed a House of Commons vote to dump it in favour of undefined "alternative arrangements". She further wrote, "I am now confident there is a route that can secure a majority in the House of Commons for leaving the European Union with a deal".
"I will be armed with a fresh mandate, new ideas and a renewed determination to agree a pragmatic solution that delivers the Brexit the British people voted for, while ensuring there is no hard border between Northern Ireland and the Republic of Ireland", said May.
"MPs said that, with changes to the Northern Ireland backstop, they would support the deal that I agreed with Brussels to take us out of the EU", May wrote.
British Prime Minister Theresa May has repeatedly reiterated London's push to stop the formation of a hard border between Northern Ireland and the Republic of Ireland after Brexit.
The EU insists that the deal "remains the best and only way to ensure an orderly withdrawal", but with the clock running down until the March 29 exit date the risks of a no-deal Brexit for both Britain and the bloc are coming into sharp focus.
MPs have voted to seek an "alternative arrangement" to guarantee the Northern Ireland border stays open after Brexit.
Japanese carmaker Nissan cancelled plans to build its new X-Trail SUV in Britain, saying while it had taken the decision for business reasons the continued uncertainty around Britain's future European Union ties was "not helping companies like ours to plan for the future".
"We want a comprehensive future relationship in place by the end of 2020 so the backstop is never used".
On Wednesday will vote on EU-great-grandson, Donald Tusk, with the Irish Prime Minister, Leo Varadkar. The next generation X-Trail will instead be made in in Japan.
Britain is scheduled to leave the European Union on March 29, but United Kingdom politicians are divided over Prime Minister Theresa May's Brexit plan. Fox told Sky News in a pre-recorded interview. "That is what Parliament instructed me to do".
But prominent eurosceptic Conservative Steve Baker said many pro-Brexit lawmakers had broader concerns about her deal.
Warnings of the consequences of a no-deal Brexit intensified last week as several multinational firms, including Airbus and Ford said jobs could suffer with an unfavourable negotiating outcome.
The backstop is meant to ensure there is no return to a hard border with Ireland, but Brexit supporters fear it will keep Britain tied to the EU's customs rules.