You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
An ouster of Special Counsel Robert Mueller would signal that Trump was acting as if he was above the law, said MoveOn.org, which is planning 800 demonstrations across the country.
Every state will have at least one "Nobody Is Above The Law" rally and at least 320,000 people have pledged to attend so far, according to MoveOn's website.
Trump would also trigger protests if he fired Deputy US Attorney General Rod Rosenstein, who is responsible for overseeing the Russia probe, or if he pardoned associates targeted in the investigation, such as former Trump campaign director Paul Manafort, MoveOn said.
Trump has been critical of the Mueller investigation, calling it a "witch hunt". He threatened to fire Mueller after the Federal Bureau of Investigation raided his personal lawyer's offices on Monday (local time), based partly on a referral by the special counsel.
US House Speaker Paul Ryan said on Wednesday he had been assured Trump did not intend to fire Mueller.
Other groups behind the planned protests include Friends of the Earth, the American Federation of Teachers, and veterans organisations, MoveOn said.
"We can't have the highest office of the land exempt from abiding by the law," Friends of the Earth US President Erich Picha said by telephone, adding that his group would support impeachment of Trump should he fire Mueller.
MoveOn said Mueller's firing would create a constitutional crisis and compared the action to President Richard Nixon's move to oust officials investigating the Watergate scandal.
The White House said on Tuesday that Trump "believes he has the power" to fire Mueller, who has widened his probe into whether the Trump campaign colluded with Moscow.
Russia has denied that it meddled in the election, and Trump has said there was no collusion between his campaign and Russia.
MoveOn is urging US lawmakers to consider impeachment proceedings against Trump should he fire officials involved in the Russia probe, the group's campaign director David Sievers said by phone.