Trump did not hold a ceremony to mark his signing the bill into law, which came as United States newspapers published excerpts from a new book by his former national security adviser, John Bolton.
Separately, the president reportedly shared with Bolton that then Defence Secretary Jim Mattis, who was also eventually dismissed and has since been a stauch critic of Trump, praised his bravery for participating in the October 2016 presidential debate right after the infamous "Access Hollywood" tape, where Trump talked about "grabbing women by the p****", was leaked.
The Republican-led Senate acquitted Mr. Trump in early February.
"This is the book Donald Trump doesn't want you to read", Simon and Schuster said.
He also wrote that Mr. Trump said invading Venezuela would be "cool" even as the US government has said it does not favour using force to topple socialist President Nicolas Maduro.
Deeply critical of the president and much of his senior team, he wrote that because staff had served him so poorly, Mr Trump "saw conspiracies behind rocks, and remained stunningly uninformed on how to run the White House, let alone the huge federal government".
Among other allegations in the book, Bolton said Trump spoke approvingly of Chinese President Xi Jinping explanation of "why he was basically building concentration camps" to intern Uighurs during a G20 meeting in Osaka in 2019 attended only by interpreters.
"Money drives a lot of people to say a lot of things", he said.
Pompeo said he had not yet read the book, "The Room Where It Happened", which the Trump administration is trying to block from publication. "Of course I would", Mr. Lighthizer said.
In one of Bolton's most memorable remarks, he dismissed the United Nations in a 1994 speech, quipping that if the 38-floor secretariat in NY "lost 10 stories, it wouldn't make a bit of difference".
Mr. Bolton cited an innumerable number of conversations in which Mr. Trump demonstrated "fundamentally unacceptable behavior that eroded the very legitimacy of the presidency".
Trump brought up the Senate episode when attacking Bolton on Fox News after excerpts from his book became public, calling the 71-year-old a "washed-up guy" to whom he gave a fresh chance.
The accusations are part of a book that the USA government on Tuesday sued to block Mr. Bolton from publishing, arguing it contained classified information and would compromise national security.
"I am hard-pressed to identify any significant Trump decision during my tenure that wasn't driven by re-election calculations", Bolton wrote.
Although Mr. Trump is publicly critical of journalists, Mr. Bolton's book quotes the U.S. President making some of his most alarming remarks to date.