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Trump, who is on a four-day state visit, said his goal was to remove trade barriers so as to give U.S. exports a fair footing in Japan.
During his comments, Japan's Nikkei 225 stock index kept its gains and ended the day modestly higher as traders interpreted a largely positive atmosphere between the two men.
Trump described the U.S. trade imbalance with Japan as "unbelievably large" but he hoped to address that.
"They are brilliant business people, brilliant negotiators and have put us in a tough spot but I think we will have a deal with Japan," Trump said.
Abe, for his part, said the two leaders had agreed to accelerate two-way trade talks.
Trump earlier explicitly linked trade and security, a connection that disturbs Japan, which puts its alliance with the U.S. at the core of its defense policies.
"It's all a balance sheet thing," Trump said at the beginning of his talks with Abe.
"When I talk about a security threat, I talk about a balance sheet," he said, adding that Japan had bought "tremendous amounts" of U.S. military gear.
On Sunday, Trump tweeted that he expected big moves on trade would wait until after Japan's upper house election in July.
"Trade-wise, I think we'll be announcing some things, probably in August, that will be very good for both countries," Trump said Monday. "We'll get the balance of trade, I think, straightened out rapidly."
Abe, who has developed close ties with Trump since the U.S. leader came into office, stressed the closeness of links.
"This visit of President Trump and Madame Trump is a golden opportunity to clearly show the unshakable bond to the whole world and inside Japan as well," Abe told the news conference.
Trump and Abe have put on a display of friendship but have policy disagreements over trade and North Korea.
The president has threatened to target Japanese automakers with high tariffs. He has also spearheaded an expensive trade dispute with China. That trade war between the world's two largest economies has hurt markets worldwide and confounded U.S. allies, including Japan and the European Union.
Such allies share U.S. concerns about Chinese practices but object to Trump's hardball tactics.
Abe and Trump also discussed North Korea.
"I personally think that lots of good things will come with North Korea. I feel that. I may be right, I may be wrong, but I feel that," Trump said Monday.
On Sunday, Trump said he was not worried about a recent missile launch by North Korea. That put him at odds with his own national security advisor, John Bolton, who said Saturday that Pyongyang's recent short-range missile tests violated U.N. Security Council resolutions. Japan shares Bolton's view.
The two leaders also discussed Iran. Abe is considering a trip to the Islamic Republic next month, domestic media said, to try to soothe rising tension between Iran and the U.S.
"We'll see what happens," Trump said. "But I know for a fact that the prime minister is very close with the leadership of Iran, and we'll see what happens."
Also Monday, Trump met with the families of Japanese citizens abducted by North Korea decades ago and told the relatives that he would work with Abe to bring the abductees home.