By Agence France-Presse
The benchmark Nikkei 225 index edged down 0.06 percent or 13.87 points to 22,453.29 in early trade while the broader Topix index was up 0.11 percent or 1.97 points at 1,775.15.
The market was weighed down by concerns over Trump's announcement later Tuesday on whether he will re-impose US sanctions on Tehran, potentially throwing the entire Iran nuclear deal into question, said Hiroaki Hiwata, strategist at Toyo Securities.
"But there are expectations for good corporate results as the Japanese earnings season peaks later this week," he added, noting that the market lacks a clear sense of direction.
European leaders and diplomats -- including Britain's Foreign Secretary Boris Johnson, who was in Washington on Monday -- have been pleading with the United States to retain the core of what Trump called a "flawed" accord.
In the 2015 pact, major powers agreed to ease some sanctions on Iran in exchange for greater scrutiny of its nuclear activities.
Trump tweeted that he would announce his decision Tuesday.
Trump has until May 12 to certify that Iran is complying with the agreement curbing its nuclear program, or clear the way for resumed US economic sanctions.
In Tokyo time the dollar fetched 108.91 yen, down from 109.88 in New York late Monday.
Toyota was down 0.31 percent at 7,178 yen while Honda was up 0.63 percent at 3,642 yen.
Takeda was up 0.76 percent at 4,494 yen hours ahead of a deadline for the Japanese pharmaceutical company's takeover bid for Irish pharmaceutical firm Shire.