Greater Manchester's mayor should "do the right thing by the people" and agree to the highest level of Covid measures, Dominic Raab has said.
The foreign secretary said Labour's Andy Burnham was "effectively trying to hold the government over a barrel over money and politics".
Mr Burnham wants more financial support for people affected by tougher rules.
Northern mayors said in a joint statement they were "united" in a "fight for what is right".
"The government is claiming that the north is divided and only interested in getting what we can for our own region. That is simply not the case," said Mr Burnham, North Tyne mayor Jamie Driscoll and Steve Rotheram, mayor of the Liverpool City Region.
Discussions between central government and local leaders over putting the region into tier three have stalled, and the leader of Manchester City Council, Sir Richard Leese, said no talks were planned for Friday.
Prime Minister Boris Johnson said he would "much rather not impose things" but he was "concerned about what's happening in Manchester, where clearly the levels of infection are rising steeply, the levels of hospitalisation are rising steeply and we do need action".
Meanwhile, Lancashire has agreed to move to tier three, the highest level of restrictions.
It comes as a scientist advising the government, Dr Jeremy Farrar, warned that the row over England's three-tier coronavirus restrictions was "very damaging to public health".
On Thursday, Mr Burnham said Greater Manchester would "stand firm" against plans to move it into tier three, calling it a "flawed" and "unfair" policy.
He said the government was "asking us to gamble our residents' jobs, homes and businesses and a large chunk of our economy on a strategy that their own experts tell them might not work".
Under tier three - the very high alert level - measures include pub closures and a ban on household mixing indoors, in private gardens and in most outdoor venues.
Mr Raab told BBC Breakfast: "Ultimately we need to take action - we can't have a situation as we have seen in Manchester where Andy Burnham is effectively trying to hold the government over a barrel over money and politics."
"I would just urge Andy Burnham to do the right thing by the people of Manchester," he said.
He said the government would "hold in reserve the ability" to impose stricter restrictions, adding that the "right response" was for Mr Burnham to "recognise that the financial package is generous".
A stand-off where lives are at risk
The stand-off between the mayor of Greater Manchester Andy Burnham and the Westminster government is fascinating.
It's not as simple as a north-south divide. Nor is it purely a clash between Labour and the Conservatives. This goes beyond a local v national government row, too.
On one side you have a long-serving MP, former health secretary and one time candidate for leader of the Labour party representing one of the party's traditional heartlands.
On the other you have a Conservative government with a big majority reliant on MPs from those and other constituencies in the north of England.
The mayor unsurprisingly wants more financial support for his region if tighter restrictions are imposed, the government needs its strategy of tiered restrictions to be seen to work.
Boris Johnson's promise to "level up" less prosperous regions of the UK plays into this, as does the chancellor's decision to reduce the extent to which he's prepared to pay people's wages.
Downing Street's decision to involve local leaders in deciding restrictions was always likely to result in negotiations like this.
But as the number of coronavirus cases continue to rise, it's no exaggeration to say lives are at risk.
Neither side will want to be seen as responsible for the virus spreading further and faster while politicians traded insults in public.
Mr Raab said that if Greater Manchester and Mr Burnham are "pulling up the drawbridge and just saying 'we're not going to proceed unless more money is coming in', I don't think that's an appropriate way to proceed".
"We can't have a situation where Andy Burnham is effectively saying unless you give us what we want, we're not going to do the right thing in terms of following the new rules which will protect the very people of Manchester he's elected to represent."
In response to the foreign secretary's comments, Mr Burnham tweeted that "it's not about what we want for ourselves," adding: "It's about what we want for low-paid and self-employed people everywhere: fairness."
The joint statement from the mayors in northern England said the government's offer to pay two-thirds of the salaries of people whose workplaces have to close would not prevent job losses.
It also said Universal Credit was not enough to "prevent severe hardship for thousands of low-paid workers before Christmas".
Manchester City Council leader Sir Richard told BBC Breakfast that "at the moment there are no meetings in the diary between us and government", adding that "we are in a bit of a vacuum".
From Saturday, people in London, Essex (apart from Southend and Thurrock), York, North East Derbyshire, Chesterfield, Erewash in Derbyshire, Elmbridge in Surrey, and Barrow-in-Furness, Cumbria, will move to the second highest tier - high alert.
This means more than half of England's population will now be living under high or very high alert restrictions.
Mr Raab told Radio 4's Today programme there was a "risk" that the government's three-tiered approach "won't work".
However, he said local leaders must "lean in" and back the system to ensure it functions as "effectively and swiftly as possible".
His comments come after Dr Farrar, who sits on the Scientific Advisory Group for Emergencies (Sage), warned making it a north-south or party political issue was "a very dangerous route".
He also said that negotiations with individual areas delayed the ability to respond to the virus, and he was more in favour of national restrictions.
Meanwhile, the Wales government is likely to introduce a two-week national lockdown, according to a union chief and a leader of Wales' largest council.
Welsh government officials - including the first minister - have been meeting local authorities and key stakeholders over a potential "circuit-breaker" - a short, limited lockdown.
It comes as a ban on travelling to Wales from coronavirus hotspots elsewhere in the UK comes into effect on Friday evening.
In Northern Ireland, pubs, restaurants and cafes will only be allowed to offer takeaway and delivery services for four weeks from 18:00 BST on Friday.
Tighter rules around face coverings have come into effect in Scotland, making them mandatory in workplace setting such as canteens.
On Thursday, a further 18,980 cases and 138 deaths within 28 days of a positive test were reported across the UK.
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