U.S. President Donald Trump and Japanese Prime Minister Shinzo Abe on Wednesday agreed to start a new dialogue on trade and investment but remained apart on discussions over Japan's exemption from new U.S. steel and aluminum tariffs and the U.S. return to the multilateral Trans-Pacific Partnership.

Despite limited progress on the trade front, Abe and Trump reaffirmed their cooperation in dealing with North Korea ahead of the U.S. president's planned summit with the North's leader Kim Jong Un, expected by early June, during their two-day summit in Florida.

Noting that the United States has a "massive trade deficit" with Japan, Trump stressed he prefers a bilateral trade deal that could open the country's markets over a multilateral one like the TPP, from which Trump withdrew the world's largest economy upon his inauguration last year.

According to U.S. Commerce Department data, the U.S. goods trade deficit with Japan totaled $68.85 billion in 2017, the third-largest among countries with which the United States generated a trade deficit.

The Japan-U.S. summit comes after Trump decided to levy stiff tariffs on steel and aluminum imports. Exemptions have been granted to several key U.S. allies but not to Japan.

Trump said Washington will not exempt Tokyo from the new tariffs unless the two countries strike a new trade deal acceptable to the United States, saying in a joint press conference at his Mar-a-Lago estate in Palm Beach, "If we can come to an arrangement on a new deal between the United States and Japan, that would certainly be something we would discuss."

Argentina, Australia, Brazil, the European Union and South Korea have joined Canada and Mexico in being granted exemptions from the stiff tariffs of 25 percent on steel imports and 10 percent on aluminum imports.

In response, Abe said Japan will continue negotiations with the United States to have its products exempted from the additional tariffs as Japanese products are "greatly contributing to U.S. industries and employment."

Last week, the U.S. president expressed interest in rejoining what is now the 11-member Comprehensive and Progressive Agreement for Trans-Pacific Partnership amid a simmering trade dispute with China, which is not a signatory.

"The media has not covered the TPP correctly. 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."

"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," Trump said.

U.S. political experts say Trump is likely to continue pressuring Japan while seeking to expand exports to the country to score points with voters in the run-up to November's midterm U.S. congressional elections.

Abe, who calls the TPP the best trade framework for Japan and the United States, fears Trump will demand the opening up of Japan's politically sensitive agricultural market and an increase in imports of U.S. products such as automobiles through a bilateral accord.

The dialogue will be led by Toshimitsu Motegi, Japan's economic and fiscal policy minister, and U.S. Trade Representative Robert Lighthizer, according to the two leaders.

Abe pledged to expand trade and investment between Japan and the United States for both countries' benefit. "I agreed with President Trump to start a consultation for a free, fair and reciprocal trade deal to realize the economic growth of the rule-based free and open Indo-Pacific region."

Trump said the two countries are "exploring ways to expedite the sale of American military equipment to Japan," making a renewed push after requesting an increase in Japan's purchases at their summit in Tokyo in November.

William Hagerty, the U.S. ambassador to Japan who attended Wednesday's meeting, told reporters the tariff exemption issue will be discussed at the new trade dialogue.

The two leaders mainly discussed North Korea on Tuesday, the opening day of their sixth face-to-face meeting.

Abe said he and Trump have agreed to keep "maximum pressure" on Pyongyang and to work together until it abandons nuclear weapons and missiles.

The White House said the two leaders "reaffirmed that North Korea needs to abandon all weapons of mass destruction and ballistic missile programs."

Japan and South Korea have been concerned that Washington is focusing only on intercontinental ballistic missiles that could strike its mainland, leaving out short- and medium-range missiles capable of hitting the two Asian allies.

Trump also promised to raise the issue of Japanese citizens abducted by North Korea in the 1970s and 1980s during his summit with the North's leader.

Earlier Wednesday, Abe and Trump played a round of golf over approximately three hours as they did in their previous two meetings in the United States and Japan last year.

Abe is due to arrive back in Japan on Friday afternoon.