A group of Tory MPs have urged Greater Manchester's mayor to "engage" with the government's regional approach to restrictions - prompting anger from some of their own colleagues.
In a letter to Andy Burnham and Labour leader Sir Keir Starmer, 20 MPs said a national lockdown would impose "severe costs" on areas with low transmission.
But four Conservative MPs for the region said the letter was unhelpful.
Ministers say Greater Manchester needs to be in the top tier of restrictions.
The letter was organised by Jerome Mayhew, MP for Broadland in Norfolk, and was signed by MPs representing constituencies currently at the lowest tier of Covid restrictions.
"It does not make sense to shut down the whole country when the virus is spiking in particular locations," the letter reads.
"Our constituents, like yours, have made many sacrifices to get - and keep - the virus under control in our areas," it adds.
Meanwhile, Liverpool City Region's metro mayor Steve Rotherham announced his area will receive an additional £44m from the government to "support local jobs and businesses" and fund a local test-and-trace service after its move to tier three - very high.
A similar package worth £42m was given to local leaders in Lancashire as part of negotiations over its move to the highest alert level.
Sir Keir has backed calls for a shorter but stricter national lockdown - also known as a circuit-breaker.
The MPs lending their names to the letter argue that a regional approach offers protection to businesses in low prevalence areas.
But Christian Wakeford, the Conservative MP for Bury South, tweeted to say the intervention was "neither wanted nor helpful".
James Daly, MP for Bury North, described the letter as "deeply disappointing... unnecessary and ill-advised".
Chris Green, the MP for Bolton West who resigned as a ministerial aide over coronavirus restrictions, said the letter was a "No 10 approved communication".
And fellow Conservative William Wragg, MP for Hazel Grove in Greater Manchester, suggested colleagues focus on their own constituencies and asked for "time and space" to work on improving the situation in Greater Manchester.
Meanwhile, Mr Burnham has accused Chancellor Rishi Sunak of being "the problem" as the Manchester mayor reiterated his call for greater financial support for workers and businesses in the area.
He told the New Statesman magazine: "I think the problem now is, to a large degree, the chancellor. I think he's made wrong judgements throughout this."
Mr Sunak has offered a 66% subsidy for those whose businesses are forced to shut by tier three restrictions.
But Mr Burnham wants a return of the original furlough scheme, which saw the Treasury pay 80% of workers wages.
He said the cost of the Eat Out to Help Out meal subsidy programme should have been paying for the furlough now.
However, the responsibility ultimately lies with the PM, Mr Burnham added.
No 10 told the BBC it had arranged a call with Mr Burnham on Sunday morning, but the Greater Manchester Mayor's office said no such call had been scheduled.