Then-president Donald Trump secretly sent COVID-19 test kits to his Russian counterpart Vladimir Putin despite a US shortage during the pandemic, and spoke multiple times with the Russian leader after leaving office, Bob Woodward said in an explosive new book out later this month.

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

In excerpts of "War" published on Tuesday by The Washington Post, where Woodward is an associate editor, he said Trump retains a personal relationship with Putin even as he campaigns for another term and Russia remains embroiled in a conflict 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.

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 -- despite US efforts to help Ukraine resist Russia and the severe deterioration of relations with Moscow.

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 ex-KGB officer 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 US election in which Trump is locked in a tight race against Vice President Kamala Harris.

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. (AFP)