Andy Burnham is calling on the Prime Minister to put the terms of any new restrictions before MPs by holding a vote in the Commons.
The Labour mayor is continuing his battle to secure increased funding in exchange for the area accepting strict new Covid-curbing measures.
He was said to have had a “constructive” conversation with Mr Johnson’s chief strategic adviser, Sir Edward Lister on Sunday afternoon, but has yet to agree on plans to move Greater Manchester into the Government’s “very high risk” category.
In a letter to the PM, Labour leader Sir Keir Starmer and other party leaders in Westminster, Mr Burnham stressed that “most places” will end up in Tier 3 at some point before a vaccine is rolled out.
Warning “this is not just a Greater Manchester issue” he insisted that “clear national entitlements” were essential to creating the “sense of fairness” needed to ensure compliance with new restrictions.
His demands include a “full and fair furlough scheme” covering 80 per cent of wages – or at least the national minimum wage; support for the self-employed and improved compensation for businesses.
“We recognise the uncertainty that this is causing and write to ask for your help in breaking the impasse and finding a fair resolution,” Mr Burnham said.
“This could be done by Parliament calling an urgent debate and vote this week to establish a cross-party consensus on what constitutes a fair financial framework for people in areas under Tier 3 restrictions.”
Following his “constructive” call with Sir Edward, the mayor is expected to hold further conversations with Downing Street on Monday.
Earlier in the day, Cabinet Office minister Michael Gove heightened tensions when he accused Mr Burnham of having engaged in political “posturing” and called for him to accept the measures “to save people’s lives”.
Mr Gove told Sky’s Sophy Ridge On Sunday he wanted to “reach an agreement with the political leadership” in Greater Manchester.
“I want them to put aside for a moment some of the political positioning that they’ve indulged in and I want them to work with us in order to ensure that we save lives and protect the NHS,” he added.
“Instead of press conferences and posturing, what we need is action to save people’s lives.”
Senior Conservative backbencher Sir Graham Brady, who is the MP for Altrincham and Sale West in Greater Manchester, told BBC Radio 4’s Broadcasting House that the region’s Labour and Tory MPs were “pretty united” in opposing Tier 3.
Mr Burnham accused the Prime Minister of having engaged in an “exaggeration” of the severity of Covid-19 in the region.
“It’s a serious situation but I don’t think it was the situation that was described by the Prime Minister on Friday evening,” the mayor told the BBC’s Andrew Marr Show.
Business leaders were also calling for greater support from the Treasury for firms forced to close in Tier 3, as well as those in Tier 2 which face “dramatically” hampered finances.
The British Chambers of Commerce told the Prime Minister that any new lockdown restrictions must come with “truly commensurate” financial support or risk “catastrophic economic consequences”.
The funding row rumbled on as new controls came into force on Saturday, meaning that 28 million people – more than half of England – are living under heightened restrictions.
Mr Johnson has been under increasing pressure to impose a short national lockdown known as a “circuit-breaker”, as recommended by the Government’s Scientific Advisory Group on Emergencies (Sage) and Labour.
Asked if the Government would take the measure on Sky’s Sophy Ridge On Sunday, Mr Gove flatly replied: “No.”
But pressed on whether the measure could be taken in the future, he said that “blanket restrictions across the country” are not merited by the disease “at the moment”.
Sage member Professor Jeremy Farrar said it is “never too late” to impose the temporary national lockdown but the best time would have been last month, when Sage advised it.
“It’s better to do it now than in a month’s time,” he told Ridge.
In other developments:
– Conservative MPs clashed over Mr Burnham’s position, with a letter written by 20 Tories in Tier 1 constituencies calling for him to “engage” with the Government’s local response being criticised by colleagues.
– Liverpool City Region’s metro mayor Steve Rotherham said the area had secured a £44 million package from the Government to support firms hit the Tier 3 lockdown.
– The UK confirmed another 16,982 coronavirus cases and a further 67 deaths from the disease – bringing the official death toll to 43,646.
– Concerns were raised after it emerged that people who have been told to self-isolate through NHS Test and Trace could have their contact details shared with police.
– Liverpool mayor Joe Anderson said his brother had died after being admitted to intensive care with Covid-19.
– Wales will have a two-week circuit-breaker imposed next week, according to a leaked letter from the Confederation of Passenger Transport.
Lancashire joined the Liverpool region in entering Tier 3 on Saturday, with pubs and bars closed unless they can serve meals and household mixing banned indoors and in gardens.
Tier 2 measures were also introduced in London, Essex, York, Elmbridge, Barrow-in-Furness, North East Derbyshire, Erewash and Chesterfield.
They prohibit people mixing inside with those from other households, including in pubs and restaurants, renewing calls from businesses for greater financial support.