“There’s a fair amount of nervousness in the White House and at the State Department about this meeting and how they manage it because they see a lot of potential risks,” said Steven Pifer, a former ambassador to Ukraine who has worked for the National Security Council and the State Department. “There is this gray cloud for the president of the investigations about collusion, so any kind of a deal is going to get the micro-scrutiny of, ‘Is this a giveaway to the Russians?’”
Mr. Trump himself does not appear to be troubled by the meeting. He has told aides he is more annoyed by the prospect of being scolded by the German chancellor, Angela Merkel, and other leaders for pulling out of the Paris climate accords and for his hard line on immigration.
Mr. Trump’s team said he might bring up Russia’s documented meddling in the 2016 election, but he is unlikely to dwell on it: Doing so would emphasize doubts about the legitimacy of his election. Aides expect him to focus on matters involving Syria, including creating safe zones, fighting the Islamic State and confronting Mr. Putin’s unwillingness to stop the government of President Bashar al-Assad from using chemical weapons against civilians.
Before the meeting between the American and Russian presidents, Secretary of State Rex W. Tillerson said late on Wednesday that the United States “is prepared to explore the possibility” of expanded cooperation with Moscow in Syria, including a discussion of establishing no-fly zones.
The official statement listed several potential “joint mechanisms” with Russia, including “no-fly zones, on the ground cease-fire observers and coordinated delivery of humanitarian assistance.”
Mr. Tillerson cautioned, though, that the United States and Russia “certainly have unresolved differences on a number of issues,” regarding Syria, and warned that no faction — presumably including the Assad government — be allowed to “illegitimately” retake or occupy areas liberated in the current offensives.
A day before Mr. Trump left Washington, the White House announced that the meeting would be a formal bilateral discussion, rather than a quick pull-aside at the economic summit gathering that some had expected.
The format benefits both. Mr. Putin, a canny one-on-one operator who once brought a Labrador to a meeting with Ms. Merkel because he knew she was afraid of dogs, will be able to take the measure of Mr. Trump.
Mr. Trump’s aides are seeking structure and predictability. They hope that a formal meeting, with aides present and an agenda, will leave less room for improvisation and relegate Russia’s meddling in the campaign to a secondary topic, behind more pressing policy concerns that the president is eager to address.
“Nobody has found the slightest evidence of collusion, any evidence the vote was tampered with, so now they have turned their obsession to Russian ‘interference,’” said Kellyanne Conway, the president’s senior counselor and former campaign manager. “I don’t think that’s what the American people are interested in.”
Still, lawmakers in both parties are pressing the president to stand tough. They signaled their wariness last month with a 98-2 vote in the Senate to codify sanctions against Russia and require that Congress review any move by the president to lift them, a step the White House is resisting.
“Let’s be clear: The Russians interfered in our election and helped elect Donald Trump president,” said Senator Jack Reed, Democrat of Rhode Island and the ranking member of the House Armed Services Committee. “There is a serious, ongoing criminal investigation into this matter. And President Trump must refrain from any unilateral concessions to Russia.”
Cognizant of the perils, the White House has planned Mr. Trump’s itinerary to counter the perception that he is too friendly with Moscow. In Warsaw on Thursday, he will deliver a major speech and meet with Central and Eastern European allies, activities calculated to demonstrate his commitment to NATO in the face of Russian aggression. But there, too, Mr. Trump will be under pressure to do what he refused to in Brussels during his first trip: explicitly endorse, on European soil, the Article 5 collective defense principle that undergirds NATO.
His advisers say that he is eager to meet with President Andrzej Duda of Poland, a center-right politician who shares Mr. Trump’s skepticism about migration, and that he sees a chance to make lucrative energy deals with Mr. Duda’s government — perhaps at the expense of Russia.
But the substance and body language of his encounter with Mr. Putin will draw the most scrutiny.
“I expect an Olympian level of macho posturing between these two leaders, who both understand the power of symbolism,” said Derek Chollet, a former assistant secretary of defense. “Putin will be very prepared for this meeting. He’s someone who is a master at manipulation.”
Mr. Putin has signaled that he will press Mr. Trump to lift sanctions imposed on Russia for its annexation of Crimea, its interference in Ukraine and its election meddling, and to hand over Russian diplomatic compounds on Long Island and in Maryland that the United States seized last year.
The potential pitfalls are more than theoretical. White House officials recall with dread the images that emerged from Mr. Trump’s May meeting with Foreign Minister Sergey V. Lavrov and Ambassador Sergey I. Kislyak of Russia in the Oval Office, which showed the president grinning, laughing and clasping hands with the Russian officials.
The biggest concern, people who have spoken recently with members of his team said, is that Mr. Trump, in trying to forge a rapport, appears to be unwittingly siding with Mr. Putin. Like Mr. Trump, Mr. Putin has expressed disdain for the news media, and he asserted in a recent interview that secretive elements within the United States government were working against the president’s agenda. Two people close to Mr. Trump said they expected the men to bond over their disdain for “fake news.”
“You don’t want to come out of there saying, ‘We’re friends, and the enemy is the deep state and the media,’” said Michael A. McFaul, a former ambassador to Russia. “If it were somebody else other than Trump, you could imagine a tough conversation about Ukraine and election meddling, but that’s probably too optimistic. Politics does constrain, I think, the parameters of the possible for any kind of major breakthrough.”