MPs and MSPs from Scotland’s capital city have written an “urgent” letter to the Labour council group amid rumours they will use Tory votes to take control of the local authority.

The letter, signed by seven SNP representatives from the Scottish and UK parliaments, says that allowing the Conservatives – who lost half their 18 former seats in the May elections – to choose the administration in Edinburgh would be “unthinkable”.

As it stands, the SNP and Greens are set to propose a formal coalition to control Edinburgh Council at a crunch vote on Thursday. The proposal was “overwhelmingly” backed by Green members at a meeting on Tuesday evening.

However, the two parties only have a combined total of 29 seats, three short of a majority on the 63-seat council.

There are rumours that Labour (13 seats) and the LibDems (12 seats) have struck a deal behind closed doors to take control of the council – something they could only do with votes from the Tory groups’ nine councillors.

The group of SNP MPs and MSPs have written to ask that Labour councillors “respect the election result” and do not use Conservative votes to take control of the city council.

Signed by Angus Robertson MSP, Ash Regan MSP, Ben Macpherson MSP, Gordon MacDonald MSP, Deidre Brock MP, Tommy Sheppard MP, and Joanna Cherry QC MP, the letter reads: “While it remains the prerogative of political groups to seek agreement with others to run the Council, as you are aware, it is only possible for Labour to form an administration, as outlined in the press, if it were supported by the Conservative councillors. Put plainly, this is unthinkable.

“The people rejected the Tories because it is led in the UK by a Prime Minister who partied in No 10 while he told the people of Edinburgh and across the UK that they could not see dying friends and relatives.

“Our residents rejected the Tories because its Scottish leader Douglas Ross has cowardly fallen into line and defended his law-breaking boss.

“They rejected the Tories because so many New Scots who called Edinburgh their home feel they are no longer welcome under Johnson’s Brexit Britain.

“They rejected the Tories because they do not want a party that cuts protections and services for the poorest and most vulnerable anywhere near local or national government.

“To be clear: any party that works with the Tories is giving credence and justification to its actions. The people of Edinburgh know this.”

Lorna Slater, the minister and Green MSP for Lothian, also urged the Labour group not to work with the Conservatives.

Slater said: "This month's election saw the Conservatives losing half of their councillors and thousands of votes in Edinburgh. Many people in our city would be shocked to see Labour and Liberal Democrat councillors lining up with the Tories to form an administration.

"It is time for progressive parties to come together and build on the achievements that were made over the last term. That is why, even at this late stage, I am urging Edinburgh's Labour and Liberal Democrat councillors to work with us, rather than the Tories."

The interventions come after Labour used Tory votes to take control of Fife Council, despite have just 20 councillors on the 75-seat local authority. The SNP won 34 in the elections, but have been forced into opposition.

Councillor Cammy Day, the leader of the Edinburgh Labour group, has been approached for comment.