US President Joe Biden expressed "complete confidence" in the United States' top general after revelations that he spoke to his Chinese counterpart twice amid concerns about then-president Donald Trump's mental state.

Biden pushed back against Republican calls to fire Joint Chiefs Chair General Mark Milley for allegedly undermining civilian control of the military in the calls last October and January as Trump refused to accept his election loss to the Democrat.

"The president has complete confidence in his leadership, his patriotism and his fidelity to our constitution," White House Press Secretary Jen Psaki told reporters.

Milley insisted his calls to Chinese General Li Zuocheng, revealed Tuesday in excerpts from a new book by Washington investigative reporters Bob Woodward and Robert Costa, were a normal part of his duties.

"The Chairman of the Joint Chiefs regularly communicates with Chiefs of Defense across the world, including with China and Russia," Milley's spokesman Colonel Dave Butler said in a statement.

"His calls with the Chinese and others in October and January were in keeping with these duties and responsibilities conveying reassurance in order to maintain strategic stability."

The Woodward-Costa book, "Peril," details worries among Milley and other top national security officials between October last year and January 20 that Trump, angered by his defeat, could initiate a conflict with China or Iran.

It also reports that Pentagon officials understood that China feared a US attack and would possibly misread US actions, like a planned military exercise, as preparations for that.

To assuage the Chinese, the book said, unbeknownst to Trump, Milley called Li to assure him that the United States was not planning action, and that the political turmoil was just the "sloppy" face of democracy.

Nuclear weapons

Even so, the book said, as tensions in Washington grew over Trump's attempts in early January to retain power, Milley called his deputies together and told them to make sure he was informed if the president sought to launch a nuclear weapon.

Faced by accusations from Republicans that Milley was usurping the president's power over the US nuclear arsenal, Butler said the meeting was simply "to remind uniformed leaders in the Pentagon of the long-established and robust procedures" on nuclear weapons.

"General Milley continues to act and advise within his authority in the lawful tradition of civilian control of the military and his oath to the Constitution," Butler said.

After excerpts from the book were published, senior Republican Senator Marco Rubio demanded in a letter that Biden fire the general.

Rubio alleged Milley "worked to actively undermine the sitting Commander in Chief of the United States Armed Forces and contemplated a treasonous leak of classified information to the Chinese Communist Party."

"These actions by General Milley demonstrate a clear lack of sound judgment, and I urge you to dismiss him immediately," he said.

Trump lashed out on Tuesday, calling Milley a crude epithet and blaming him for the chaotic US withdrawal from Afghanistan in August.

"I assume that he would be tried for treason in that he would have been dealing with his Chinese counterpart behind the president's back," Trump said in a statement.