Washington DC - Then-president Donald Trump secretly sent Covid test kits to Vladimir Putin despite a US shortage during the pandemic, and spoke multiple times with the Russian leader after leaving office, Bob Woodward says in an explosive new book.

The famed reporter's opus also chronicles some of President Joe Biden's own acknowledged missteps and his struggle to prevent escalation of conflict in the Middle East, including exasperation with Prime Minister Benjamin Netanyahu over futile efforts to get Israel to agree to a ceasefire.

In excerpts of War published Tuesday by The Washington Post, where Woodward is an associate editor, he says Trump retains a personal relationship with Putin even as he campaigns for another term and the Russian president conducts a war against Ukraine.

With the coronavirus raging in 2020, Trump sent a batch of coveted tests to his counterpart in Moscow. Putin accepted the supplies but sought to avoid political fallout for Trump, urging he not reveal the dispatch of medical equipment, the book says.

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According to Woodward, Putin told Trump: "I don't want you to tell anybody because people will get mad at you, not me."

Woodward also cites an unnamed Trump aide who indicated the Republican leader may have spoken to Putin up to seven times since leaving the White House in 2021.

The Post, reporting Woodward's account, said that at one point in early 2024, Trump ordered an aide out of his office in his Mar-a-Lago residence in Florida because he wanted to hold a private call with Putin.

At a campaign event Tuesday for Pennsylvania Senator Bob Casey, Biden said the way Trump handled the pandemic was a "disgrace."

"Over a million people died. But guess what... he called his good friend, Putin, not a joke, and made sure he had the tests," Biden said.

War hits bookshelves October 15, just three weeks before a critical election in which Trump is locked in a tight race against Vice President Kamala Harris.

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While Democrat Harris appears in the book, she is seen in a supporting role to Biden "and hardly determining foreign policy herself," the Post reported.

Harris, asked about the book Tuesday by popular radio host Howard Stern, said Trump had been "played" and manipulated during a health calamity that saw Americans "dying by the hundreds every day."

"Everybody was scrambling to get kits (and Trump) is sending them to Russia, to a murderous dictator for his personal use," Harris said.

Woodward has chronicled American presidencies for 50 years, and this is his fourth book since Trump's upset victory in 2016. Woodward began his presidential reportages with Richard Nixon, who was undone by the 1970s Watergate scandal exposed by Woodward and Post colleague Carl Bernstein.

Woodward concluded that Trump's interactions with an authoritarian president at war with a US ally make him more unfit for the presidency than Nixon.

"Trump was the most reckless and impulsive president in American history and is demonstrating the very same character as a presidential candidate in 2024," Woodward writes.

The Trump campaign blasted the book as "made-up stories."

They are "the work of a truly demented and deranged man who suffers from a debilitating case of Trump Derangement Syndrome," spokesperson Steven Cheung told AFP.

Trump has repeatedly praised Putin. During the 2016 campaign, the Republican memorably urged Moscow to "find" thousands of Hillary Clinton's emails.

US intelligence agencies later concluded Russia had meddled in that election in Trump's favor, although a special counsel's investigation found no conspiracy between the Trump camp and Moscow.

According to CNN, which obtained a pre-release book copy, Woodward quotes the outwardly mild-mannered Biden swearing as he discusses his personal and political challenges.

Biden called Putin "the epitome of evil," blasted Netanyahu as a "liar," and said he "should never have picked" Merrick Garland as US attorney general.