Former foreign secretary Boris Johnson says it would be “absurd” to hold a vote on the PM’s Brexit deal before attempting further talks with the EU.
Writing in the Daily Telegraph, the leading Brexiteer says: “There is an EU summit this week. It is not too late to get real change to the backstop.”
The backstop is a contingency plan for the Irish border, but has proved a sticking point in getting a final deal.
The PM’s plan is expected to be voted on for a third time in the coming days.
However, Chancellor Philip Hammond said it would only return to the Commons this week if it had support from many previously rebelling Tories and from the 10 MPs from the Democratic Unionist Party.
The DUP has previously been very critical of the backstop plan, repeatedly saying it will not accept any additional Northern Ireland-only checks.
Negotiations with the DUP, whose MPs prop up the Tory government, are expected to continue on Monday, although Downing Street said a formal meeting was not scheduled.
Meanwhile, Labour leader Jeremy Corbyn will have a series of meetings with other Westminster leaders and some influential backbenchers in an effort to find a cross-party compromise.
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Earlier last week, MPs rejected Theresa May’s deal again – this time by 149 votes – and then backed plans to rule out leaving the EU without a deal.
They also voted in favour of an extension to the process – either until 30 June if Mrs May’s deal is supported before 20 March, or a longer one that could include taking part in European elections if MPs reject her plan for a third time.
But legally the UK is still due to leave the EU on 29 March.
All 27 EU member states would have to agree to an extension – and the countries’ leaders are expected to discuss it at a summit on Thursday.
Mr Johnson, writing in his weekly Daily Telegraph column, said that further changes were needed to the Irish backstop in Mrs May’s withdrawal deal to break the impasse in Parliament.
He said the backstop arrangement left the UK vulnerable to “an indefinite means of blackmail” by the EU.
“If we agree this deal – and unless we have a radical change in our approach to the negotiations – we face an even greater humiliation in the second phase,” he said.
He added that the government should outline its strategy for talks on the future relationship with the EU to “reassure its understandably doubtful MPs by answering some basic questions about the next phase of the negotiations”.
Another Tory MP, Chris Green, told BBC Radio 4’s Westminster Hour that he would probably vote against the deal but was still weighing up the decision – although a shift in the DUP’s stance would have a “big impact”.
He added that the implications of rejecting the deal for a third time weighed heavily on him “because it could lead to a general election, and we don’t know how that will pan out”.
The possibility of Brexit being delayed or overturned in another referendum has seen some MPs reluctantly back Mrs May’s deal.
This includes former Cabinet minister Esther McVey, who told Sky’s Sophy Ridge programme that she would “hold my nose” and vote for it.
A group of 15 Tory MPs from Leave-backing constituencies, including former Brexit Secretary David Davis, wrote a letter urging colleagues to back the deal to ensure Brexit goes ahead.
But so far the number of Tories publicly switching positions falls far short of the 75 MPs Mrs May needs to switch sides.
Brexit: Not too late for real change to PM’s deal – Johnson}