The prime minister is to chair a meeting of the Cobra emergency committee later in response to floods in northern England.
The Environment Agency has 39 flood warnings in place, including five severe warnings on the River Don in South Yorkshire.
About 400 homes have been flooded and 1,200 properties evacuated.
Prior to the government’s announcement, Labour leader Jeremy Corbyn had called on Boris Johnson to convene Cobra.
Mr Corbyn urged the prime minister to “take personal charge” of the situation and said he disagreed with Mr Johnson’s assessment at the weekend that the floods were not “a national emergency”.
He wrote to Mr Johnson, saying: “If this had happened in Surrey, not Yorkshire or the East Midlands, it seems far more likely that a national emergency would have been declared.”
A government spokesman said: “The prime minister will chair an emergency meeting… [Tuesday] to discuss the response to recent flooding.”
A yellow warning for rain remains in place over parts of Yorkshire and the East Midlands for Monday, Tuesday and Thursday, and an emergency appeal to support “displaced” families has raised almost £50,000.
Doncaster Council has called for people to evacuate the village of Fishlake, saying it “can only offer dedicated support to people who are not in an area where there is a threat to life”.
But farmers say they are unable to leave as they need to care for their livestock.
Joe Howslam, 23, told the BBC: “I live in Fishlake with my parents, brother and sister, but we’ve all had to move out.
“In the history of Fishlake it’s never been this bad, according to some of the older members of our village.
“I’m an HGV mechanic and we’ve run a family farm, so I borrowed a tractor on Saturday and helped rescue a few people. I even rescued my dad from the top window of the house.
“There’s about two feet of water downstairs, so the washing machine, dishwasher, etc. are all under water and ruined. We managed to get some things out of the living room but not all of it.”
He said he had heard reports of looting in the village, but added family members regularly return to the area.
Four Environment Agency pumps are in Fishlake to take out floodwater from the village.
The local church is collecting food to distribute to residents and roast dinners were delivered on Sunday to those who had remained in their homes.
Empty coffins were seen floating inside the workshop of a flooded funeral parlour in the village.
Tractors and boats have been used to get around the village, with many roads in the area under floodwater.
According to the Salvation Army, some people have been rescued from their homes by boat since the early hours of Saturday, but others remain in their properties, while military helicopters have been used to help boost flood defences in the area.
Twelve flood warnings remain in Lincolnshire where more than 1,000 acres have been flooded by Barlings Eau and some farms are cut off, with some train lines still blocked by high water.
Northern said its services into Rotherham Central were not running until further notice, with reduced services between Doncaster and Sheffield. CrossCountry’s trains are being diverted away from Doncaster.
Doncaster Council said a number of roads remained closed.
The RSPCA has been involved in a rescue operation to save 60 swans following an oil spillage caused by flooding in Rotherham.
Further south, parts of Derbyshire are still affected by flooding.
Areas around Matlock – where former High Sherriff of Derbyshire Annie Hall was swept to her death by the flooded River Derwent – are continuing their clean-up efforts, with further rain over the weekend leaving standing water along a number of roads.
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