WARSAW — President Trump arrived in Europe on Wednesday for three days of diplomacy that will culminate in a meeting with President Vladimir V. Putin of Russia, which has the potential for global repercussions and political fallout back home.

Even his top aides do not know precisely what Mr. Trump will decide to say or do when he and Mr. Putin meet face to face on Friday on the sidelines of the Group of 20 economic summit gathering in Hamburg, Germany. And that is what most worries those advisers as well as officials across his administration as Mr. Trump begins his second foreign trip as president, stopping first in Warsaw to give an address on Thursday and then heading to Hamburg.

The highly anticipated conversation with Mr. Putin is in many ways a necessity, given the critical disputes separating the United States and Russia. But it also poses risks for Mr. Trump, who faces a web of investigations into his campaign’s possible links to Russia, as well as questions about his willingness to take on Moscow for its military aggression and election meddling on his behalf. The air of uncertainty about the meeting is only heightened by the president’s propensity for unpredictable utterances and awkward optics.

And it is not the only charged encounter awaiting Mr. Trump this week. Following North Korea’s launch on Tuesday of an intercontinental ballistic missile, he also faces new pressure to act on a threat from Pyongyang that has long confounded American presidents, and that he has few appealing ways to address. He is scheduled to meet in Hamburg with President Xi Jinping of China, as he complains that Beijing has not done enough to rein in North Korea.