Donald Trump was determined during his presidency to cozy up to Vladimir Putin despite objections by advisers, a former top aide claims in a new book, according to an excerpt published Saturday.

The new behind-the-scenes details from H.R. McMaster, Trump's second national security adviser, come as Americans are set to decide whether the former president should return to the White House and as US officials warn of fresh foreign election meddling.

"After over a year in this job, I cannot understand Putin's hold on Trump," McMaster, in an excerpt from his memoir published in the Wall Street Journal, says he told his wife in March 2018.

A former lieutenant-general, McMaster became Trump's national security adviser in February 2017, and says that from the beginning, discussions of Vladimir Putin and Russia "were difficult to have with the president."

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He says Trump connected "all topics involving Russia" to the federal investigation into Moscow's interference in the 2016 election and possible ties with Trump's campaign, a probe that would dog his entire presidency.

McMaster says an "overconfident" President Trump sought early in his administration to improve relations with Russia by building a personal rapport with Putin.

But the Russian president, "a ruthless former KGB operator, played to Trump's ego and insecurities with flattery," McMaster says.

"Trump had revealed his vulnerability to this approach, his affinity for strongmen, and his belief that he alone could forge a good relationship with Putin," he added.

McMaster detailed several instances of friction with Trump over his approach toward Putin, with the disagreements ultimately leading to his dismissal.

Following Putin's election to a fourth term in March 2018, McMaster says Trump wanted to congratulate him by phone, but that he explained to the president that the vote had been rigged. A call was scheduled nonetheless.

Before Trump called Putin, McMaster says he warned him about the conversation potentially being spun by the Kremlin as tacit support of the election process and to boost Russia's image, suffering at the time over an assassination attempt on UK soil.

He said he asked Trump: "As Russia tries to delegitimize our legitimate elections, why would you help him legitimize his illegitimate election?"

Trump nonetheless called Putin and congratulated him, and then requested the Russian president be invited to the White House.

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Trump's aversion to McMaster, he said, "was because I was the principal voice telling him that Putin was using him and other politicians in both parties in an effort to shake Americans' confidence in our democratic principles, institutions, and processes."

McMaster was replaced just days later by John Bolton, who was also fired about a year and a half later.

While Trump had four national security advisers during his term, President Joe Biden has had one since taking office in 2021.

"With Donald Trump, most everybody gets used up, and my time had come," McMaster wrote.