LONDON - British Prime Minister Theresa May urged her increasingly mutinous party on Monday to back her strategy over Brexit, insisting a deal with the EU was close even as she once again rejected the bloc's proposal for the Irish border.

In an article in the mass-selling The Sun tabloid, she argued that her strategy for pulling Britain out of the European Union was "not about me" but based on the "national interest".

But opposition from all sides has stepped up at home since a Brussels summit last week failed to make a breakthrough, raising fears Britain could be heading for a deeply damaging "no deal" exit next March.

Talk of a leadership challenge from within her Conservative party reached fever pitch at the weekend, with one newspaper quoting an unnamed MP saying May was entering "the killing zone". "The Brexit talks are not about me or my personal fortunes. They're about the national interest - and that means making the right choices, not the easy ones," May wrote.

No compromise on Ireland

She will later Monday update the House of Commons on the state of Brexit talks, where she will tell MPs that "95 percent" of the divorce deal is now agreed.

But Brussels and London still disagree on how to keep open the land border between British Northern Ireland and EU-member Ireland - and May emphasised she will not compromise on this.

"I've been very clear that this must be achieved without creating any kind of border between Northern Ireland and the rest of the UK," she wrote in The Sun.

"Doing so would undermine our precious Union and put at risk the hard-won peace" in the province, which was plagued by three decades of violence in which 3,500 people died.

The EU wants to keep Northern Ireland aligned with its customs rules and regulations until a wider trade deal can be agreed that removes the need for frontier checks.

London rejects this, offering instead a UK-wide solution - but insists this can only be temporary, something the EU says it cannot agree to.

Eurosceptic Conservatives fear the dispute could force Britain into a never-ending customs union with the EU after Brexit, leaving it unable to conduct its own trade policy. A plan mooted in Brussels last week to extend the post-transition to resolve the matter only added to their fears. May held two conference calls with her cabinet ministers over the weekend in a bid to allay their concerns. But as the Brexit deal nears, the pressure is growing on her critics to put up or shut up.

Conservative rebellion

May's Northern Irish allies, the Democratic Unionist Party (DUP), have already raised the stakes by threatening to vote against next week's budget if the deal results in any special status for the province. Up to 41 eurosceptic Conservative MP could this week also back an attempt to enshrine the pledge on Northern Ireland into law, according to their group, StandUp4Brexit.

An amendment to an existing bill would make it impossible to implement "any trade or regulatory barriers" between Northern Ireland and the rest of Britain without agreement by the province's assembly.

 The assembly has not sat since January 2017 and the DUP could likely block any such approval.

Pressure is also growing from those who were never reconciled to Brexit.

Almost 700,000 anti-Brexit protesters hit the streets of London on Saturday, organisers said - the largest demonstration since 750,000 people demonstrated against the Iraq war in 2003.

Backlash at violent briefings against PM

"Bring your own noose" as you enter the "killing zone" - anonymous briefings against British Prime Minister Theresa May are nothing new, but the ferocity of the latest batch sparked a fierce backlash Monday.

Many of May's critics and her allies rounded on unnamed pro-Brexit members of her Conservative party who used violent language to attack her Brexit strategy in the weekend newspapers.

One MP was quoted as saying that she should "bring her own noose" to a meeting later this week of Conservative lawmakers.

Another newspaper quoted an MP as saying that May was entering the "killing zone", with another adding: "Assassination is in the air".

A former minister reportedly said: "The moment is coming when the knife gets heated, stuck in her front and twisted. She'll be dead soon."

The comments drew a chorus of outrage from fellow Conservative MPs, with pro-Europeans through to ardentBrexiteers condemning them as "totally unacceptable".

Senior lawmaker Robert Halfon said it was "a shame on the Conservative party".

Opposition Labour MP Yvette Cooper said it was "dehumanising" and "normalising violence in public debate", noting the 2016 murder of her colleague Jo Cox by a far-right sympathiser.

Conservative MP Mark Francois, a member of a hardline eurosceptic group, said the language was "unacceptable".

But he told the BBC: "The problem is that there is a lot of frustration on the backbenches at the moment, both among Leavers and Remainers, at the general state of play." Fellow Brexiteer Conservative Andrew Bridgen warned: "At the moment that (language) is unhelpful. It won't persuade colleagues to back a change of leadership.

"It's actually going to be counter-productive at this point." The prime minister's spokesman refused to comment on anonymous briefings, but said: "Personal vitriol has no place in politics."