US President Donald Trump and Japanese Prime Minister Shinzo Abe say they’ve agreed to intensify trade consultations between the two longtime allies, with an aim to expand investment and trade between their countries.

“President Trump and I agreed to start talks for free, fair and reciprocal trade deals,” Abe said at a joint news conference with Trump.

Trump reaffirmed his desire at the news conference to address trade imbalances with Japan, saying he preferred one-on-one talks to negotiate a bilateral deal aimed at trimming the US trade deficit.

Last month Trump imposed a 25 per cent tariff on steel imports and a 10 per cent tariff on aluminium imports.

He said the tariffs had brought many countries to the negotiating able and that he may remove them from Japanese imports if the two countries can come to a trade agreement.

Temporary tariff exemptions have been granted to several other US allies, including Australia, but not Japan.

Japanese stocks rallied to a seven-week high, partly due to relief that Trump did not mention the value of the yen or criticise Japan’s monetary policy.

While the leaders said they had agreed to have top advisers pursue talks, Abe made clear that differences remained in each country’s approach.

“On the US side, they are interested in a bilateral deal,” Abe told reporters. “Our country’s position is that TPP is the best for both of our countries,” he added, referring to the Trans-Pacific Partnership trade deal.

The TPP was sought by former president Barack Obama. Trump abandoned it during his first weeks in office, saying it was not a good deal for the United States.

“I don’t want to go back into TPP, but if they offered us a deal that I can’t refuse on behalf of the United States, I would do it,” Trump said.

“But I like bilateral better. I think it’s better for our country. I think it’s better for our workers, and I much would prefer a bilateral deal, a deal directly with Japan,” he added.

Abe said that Japanese steel and aluminium did not “exert any negative influence” on US security.

“It’s our position that the quality of Japanese products is high and many of these products are difficult to be replaced with. They are greatly contributing to US industries and employment,” Abe said.