The two leaders are discussing topics of bilateral concern, including Trump's upcoming meeting with Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK), and bilateral trade.
Experts say while the two sides try to seek common ground, noticeable differences will linger.
TRUMP-KIM MEETING
On Tuesday afternoon, Trump and Abe, who was on a two-day working visit in the United States, held a one-to-one meeting followed by a restricted bilateral meeting.
Trump told reporters before their restricted bilateral meeting that during the two days the two leaders would talk about the situation on the Korean Peninsula and bilateral trade, among others.
Trump said that he and Abe had developed "a very close relationship," adding that U.S.-Japan ties "have never been closer than they are right now."
Trump also said that he looked forward to meeting with Kim, hoping "that will be a success." The Trump-Kim meeting has been planned to take place in May or early June.
Referring to the upcoming meeting, Abe said that he hoped "there will be tangible progress toward resolving the outstanding issues of concern, including nuclear issues, missile issues, as well as the abductions issue, which is the Japanese top priority issue."
The DPRK acknowledged in 2002 that it had abducted 13 Japanese nationals in the 1970s and 1980s. Talks on the issue were shelved in December 2012, when the country launched a long-range missile.
Acknowledging Japan's concern, Trump responded that Washington will "bring up the abductees" in his meeting with Kim.
"Abe had established the best personal relationship with Trump and yet felt blind-sided by Trump's sudden and impetuous decision to accept the North Korean (the DPRK's) invitation for a summit meeting," Bruce Klingner, senior research fellow for Northeast Asia at conservative think tank the Heritage Foundation's Asian Studies Center, told Xinhua.
The main purpose of Abe's trip may be communicating to Trump the importance of Japanese security interests in the upcoming summit with Kim, Douglas Paal, vice president for studies at the Carnegie Endowment for International Peace, told Xinhua.
Tokyo was concerned that its interests might be overlooked by Washington. "One big concern is that Trump might strike a deal with Kim that reduces the threat to the United States but does not change the growing threat to Japan," said Paal.
Abe would also "seek to ensure that Trump agrees that Japan needs to be present at any multinational negotiations" regarding the Korean Peninsula issue, Jeffrey W. Hornung, political scientist at The RAND Corporation, told Xinhua.
BILATERAL TRADE
The Trump-Abe discussion was the second of its kind between the two since last year.
While the DPRK remains a primary focus of the meeting, trade issues are also on top of the agenda.
"He (Abe) would like to resolve the steel/aluminum tariffs issue which implies Japan is not an ally," said Paal.
"Trump never lets go of the trade deficit as an issue, and seems to have an underlying skepticism of the Japanese in general," said the scholar.
While Trump gave exemptions to other U.S. allies, such as South Korea, Australia and Canada, he did not do the same for Japan.
"Abe had invested significant political capital to develop the relationship with Trump but was politically wounded when Trump withdrew from the TPP (Trans-Pacific Partnership, an 11-nation Free Trade Agreement that will eliminate 98 percent of tariffs in the trade zone) as well not giving Japan an exemption from Trump's protectionist tariff initiative," said Klingner.
White House economic adviser Larry Kudlow said Tuesday that the United States was expecting a free trade deal with Japan at some point, while acknowledging that the two countries had some differences on trade.
"We have certain disagreements with respect to some of the trading issues. We'll iron those out hopefully," Kudlow told reporters during a briefing ahead of the Trump-Abe meeting.
"Should his efforts to cultivate a friendship with Trump prove to pay no dividends, Abe will surely be open to political criticism that would further hurt his chances at successfully running for a third term as his party's leader in the fall," said Klingner.
