Nearly 100,000 acres have been destroyed by wildfires in recent weeks, and thousands have been forced from their homes. Although there were no reports of any casualties so far, the BBC reported on Monday
In a series of tweets, Trump blamed Newsom, saying he had done a "terrible job of forest management".
Several of this year's major wildfires have burned in unforested areas.
"Every year, as the fire's (sic) rage & California burns, it is the same thing - and then he comes to the Federal Government for $$$ help. No more. Get your act together Governor," Trump tweeted.
Newsom, who has been highly critical of Trump's environmental policies, responded: "You don't believe in climate change. You are excused from this conversation."
The President had made a similar threat to cut federal aid last year, when the most deadly fire in California's history killed 86 people.
Meanwhile, firefighters have contained about half of the Maria Fire, the major blaze in southern California which broke out on October 31, the BBC said.
It has burned more than 9,400 acres, the Ventura County Fire Department said on Sunday.
The largest blaze, the Kincade Fire in Sonoma County, was 76 per cent contained on Sunday after burning nearly 80,000 acres since it started on October 23, according to officials.
All evacuation orders were lifted on Saturday.
( With inputs from IANS )