Boris Johnson warned there will be "further rain" overnight as he visited flood-hit Didsbury to see the impact of Storm Christoph.
He suggested a major tree-planting programme could help protect against flooding in the long-term.
And Number 10 promised the Army were available to assist if necessary.
The Prime Minister's spokesman said: "The military are always available to provide extra support if needed.”
During the visit, Mr Johnson said: "We are very worried, obviously, about the risk of flooding every year."
He thanked the Environment Agency for their "amazing preparations" and the effort to evacuate people overnight, but warned "there will be further rain overnight".
The Prime Minister said the Environment Agency had used used sluice gates and "improvised emergency flood defences to protect homes".
"I think 10,000 homes in the Manchester area, in the Didsbury area, have been protected just as a result of what they have been doing overnight.
"There will be more to come, there will be further rain next week, so it is vital that people who are in potentially affected areas follow the advice and get the Environment Agency flood alerts where they can."
He added: "One idea that everybody in the Environment Agency talks about, and I believe in absolutely passionately, is planting trees on the higher ground to help absorb some of that rainfall, to help mitigate the effects of flooding.
"This Government has a very ambitious tree-planting programme, but, in my view, we're not going fast enough.
"As the spring comes and we come out of the pandemic, we're going to want to see a lot done to build in long-term resilience against flooding and against climate change, and planting trees is a big part of that."
The Prime Minister defended the Government's record on funding flood defences.
"A huge amount has been done here in Greater Manchester, another £60 million has been put in to protecting the Greater Manchester area," he said.
"You can see the defences that we have in place to protect people's homes and people's lives.
"But, be in no doubt, everybody who visits a flood area, anybody who has been through a flood knows the huge psychological, emotional and financial cost of flooding to people."
A further £20 million will be invested for the Greater Manchester area as part of a £5.2 billion programme of flood defences over the next six years, he said.
