Palestinian-backed plans for a UN security council vote designed to show international opposition to Donald Trump’s Middle East peace plan have been shelved after the US and the UK raised separate objections to the draft text.

In what was seen as a key test of the diplomatic support for Trump’s “ultimate deal”, Tunisia, with Arab League and Palestinian support, had tabled a resolution saying it breached basic undertakings to the Palestinian people.

Without the resolution going to a vote on Tuesday, the Palestinian president Mahmoud Abbas instead used his speaking slot to rail against the US administration, which he has long criticised as brazenly in favour of Israel’s government.

Holding up a map of Trump’s plan, showing small pockets of land allocated for Palestinians, Abbas described it as cutting up any future state of Palestine into “Swiss cheese”.

“If you impose peace it will not last, it cannot last,” he said of the plan, which has been endorsed by Israel.

Hours before he spoke, a few thousand Palestinians protested in the West Bank city of Ramallah and in the Gaza Strip against the US initiative. A poll released on Tuesday, the first since Trump presented his “vision for peace” last month, found 94% of Palestinians reject it.

Despite the Palestinian position, Israel plans to soon begin implementing some of the most contentious aspects of the deal, including annexing large sections of occupied Palestinian territory given to it under the terms. Washington has said it supports such moves, if done in consultation, while other world powers has warned that land grabs would be illegal.

In a joint statement, UN Security Council members Belgium, Estonia, France and Germany said that any annexation would also challenge “the prospects for just, comprehensive and lasting peace”.

The diplomatic episode over the failed resolution vote was seen as a key test of whether post-Brexit Britain would stick to its longstanding positions on the Middle East peace process or instead seek to avoid a clash with the Trump administration by abstaining on the Tunisian text.

In an effort to find a compromise the UK on Monday called for changes to the draft text, including the insertion of a call for both Israel and the Palestinians to return to negotiations. The formula would allow the British not to endorse the Trump plan but to portray it as a possible basis for negotiations.

The US set out an array of objections to the Tunisian text and indicated it would veto the resolution if it was not rewritten.

Blocking the vote is likely to be seen as a rare diplomatic success for the US at the UN on the Middle East issue.

Washington has been putting pressure on UN security council delegations for days in an attempt to ensure it would not be isolated in Tuesday’s planned vote. Such has been the pressure that last week the new Tunisian government felt forced to recall its highly experienced and respected UN ambassador, Moncef Baati.

Jared Kushner, Trump’s son-in-law and the architect of the plan, met key diplomats on Thursday in New York to seek support and seems to have faced resistance from European countries including France which asked why the Palestinians had not been consulted.

Josep Borrell, the EU’s foreign policy chief, caused a stir when he condemned the US plan, saying future Israeli annexations of West Bank settlements could not pass unchallenged, and reiterated the EU’s commitment to a viable two-state solution.

Last month in the House of Commons, Boris Johnson said the Trump plan had its merits though “no peace plan is perfect”. The UK foreign secretary, Dominic Raab, described the plan as “clearly a serious proposal, reflecting extensive time and effort”.

Neither remark represented an endorsement, and British diplomats have been working to test the degree of flexibility the administration is willing to show about the plan. One western diplomat said different parts of the administration showed different degrees of flexibility.

“It may be the Americans view this as similar to a real estate deal. You bid low and expect the other side to come back high,” one said.

Britain has in the past broken with the US on the issue, including when Johnson was foreign secretary and the UK rejected a US proposal to recognise Jerusalem as the capital of Israel.