Trump is also looking forward to presenting a trophy to the victor of Tokyo's spring sumo wrestling tournament after witnessing the event from ringside seats, White House officials said.
Trump arrived in Japan on Saturday for a largely ceremonial state visit meant to showcase strong ties despite simmering trade tensions.
Trump arrived shortly after a relatively strong natural disaster rattled Tokyo. Trump is seeking a bilateral trade deal with Japan, after pulling the USA out of the 12-nation Trans-Pacific Partnership.
Trump will also play golf with Abe and have the chance to present a "Trump Cup" at a sumo wrestling championship Sunday.
"The Department of Justice has provided a legal opinion stating that, based on long-standing, bipartisan and constitutional precedent, the former counsel to the president can not be forced to give such testimony, and Mr. McGahn has been directed to act accordingly", White House press secretary Sarah Sanders said in a statement.
"Prime Minister Abe said to me, very specifically, 'You are the guest of honor.' There's only one guest of honor".
Mr Trump had predicted that a US-Japan trade deal could be finalised during his trip.
He nonetheless portrayed the negotiations in a positive light in his remarks to the business group. "I don't think I'd ever see Doral again", he said at a rally February 2016, referencing golf courses. "And we're getting closer", he said, while urging the business leaders to invest more in the US. "Nadler issued subpoenas for more Trump officials - former White House communications director Hope Hicks and Annie Donaldson, a former aide in the White House counsel's office - for documents and testimony", the AP said.
The president and first lady Melania Trump, wearing a white printed dress, were greeted at the airport by Japan's Minister of Foreign Affairs Taro Kono, the U.S. Ambassador to Japan William F. Hagerty and other members of the United States and Japanese diplomatic corps at about 4 p.m. local time. -Japanese relationship "has never been more powerful, never been closer".
Some parts of the subpoenas have been included in court filings.
Mr Trump will also meet outgoing PM Theresa May and other royals including the Duke and Duchess of Cornwall, the Duke and Duchess of Cambridge and the Duke of Sussex.
Bolton said Trump and Abe would "talk about making sure the integrity of the Security Council resolutions are maintained". That raised alarm bells in Japan, where short-range missiles pose a serious threat.
Earlier Wednesday, Trump lashed out at Democrats for what he claimed were attempts to harass and undermine his presidency, declaring during an irate appearance in the Rose Garden he could no longer work with them as they proceed in their investigations.
Deutsche Bank has reportedly allowed Donald Trump to borrow billions of dollars over the past few decades, while other major banks would not due to his bankruptcies.
Security is tightened in Tokyo ahead of Trump's visit.
US President Donald Trump arrived in Japan Saturday for a four-day trip likely to be dominated by warm words and friendly images, but relatively light on substantive progress over trade.
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