Takaichi -- Japan's first woman prime minister -- pulled out all the stops for Trump in her opening test on the international stage, and even announced she would nominate him for a Nobel Peace Prize, the White House said.
In return, Trump, who was meeting conservative Takaichi for the first time on an Asia tour that aims for a deal with China, said Washington was an ally of the "strongest level".
"It's a great honour to be with you, especially so early in what will be, I think, one of the greatest prime ministers," Trump told Takaichi at the Akasaka Palace state guest house.
Takaichi praised Trump's efforts towards a ceasefire between Thailand and Cambodia and his "unprecedented historic achievement" of the Gaza deal.
"I would like to realise a new golden age of the Japan-US Alliance, where both Japan and the United States will become stronger and also more prosperous," she said.
The two sides also signed an agreement aimed at "achieving resilience and security of critical minerals and rare earths supply chains", a statement said.
Beijing this month announced sweeping restrictions on the rare earths industry, prompting Trump to threaten 100 percent tariffs on imports from China in retaliation.
After meeting with Takaichi, Trump then swiftly headed to meet with families of Japanese abducted by North Korea decades ago, where he said "the US is with them all the way" as they asked for help to find their loved ones.
After years of denial, North Korea admitted in 2002 that it had sent agents to kidnap 13 Japanese people who were used to train spies in Japanese language and customs. Japan says it also abducted others.
- Trade talks -
Trump arrived in Tokyo on Monday for a visit sandwiched between a trip to Malaysia and a meeting in South Korea with Chinese counterpart Xi Jinping that could ease the bruising trade war.
Negotiators from Beijing and Washington have both confirmed a "framework" has been agreed between the world's two biggest economies.
In Tokyo, Trump and Takaichi were expected to focus on security and trade between their allied countries.
Takashi Ito, a 58-year-old Tokyo resident, said that "what's important is finding some kind of middle ground" on trade.
"Simply pushing to raise tariffs has already created various issues."
On security, long-pacifist Japan is adopting a more muscular military stance as relations with China worsen.
Takaichi, a China hawk who last week became the first woman to serve as Japan's prime minister, said her government would achieve its target of spending two percent of gross domestic product on defence this year -- two years ahead of schedule.
The United States, which has around 60,000 military personnel in Japan, wants Tokyo to spend even more, potentially matching the five percent of GDP pledged by NATO members in June.
Yee Kuang Heng, a professor at the University of Tokyo's Graduate School of Public Policy, told AFP that in a bid to "deflect US pressure" on Japan to boost defence spending, Takaichi has "preemptively" brought forward the target.
Apart from his meeting with Takaichi, Trump is due to deliver a speech on Tuesday on the USS George Washington aircraft carrier, docked at the US naval base Yokosuka.
He will also have dinner with business leaders, likely including the chairman of carmaker Toyota.
- 'Phenomenal' -
Most Japanese imports into the United States are subject to tariffs of 15 percent, less painful than the 25 percent first threatened.
But the levies still contributed to a 24-percent slump in US-bound car exports in September in value terms year-on-year.
The car industry accounts for around eight percent of jobs in Japan.
Under the terms of a July trade deal shared by the White House, Japan is also expected to invest $550 billion in the United States.
Takaichi is at pains to establish a good relationship with Trump, who had a close personal relationship with assassinated former premier Shinzo Abe.
Abe's alleged killer Tetsuya Yamagami was due to go on trial in the western city of Nara -- also Takaichi's hometown -- more than three years after the fatal shooting.
The greatest prize for Trump -- and for global markets -- remains a China trade deal.
Trump is due to meet Xi on Thursday in South Korea for their first face-to-face talks since the 79-year-old Republican's return to office in January.
aue-bur-aph-stu/mtp
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