But if Mr. Trump agrees to work with Mr. Putin despite a list of Russian transgressions beginning with the annexation of Crimea and ending with its interference in the 2016 presidential election, he will also look weak while Mr. Putin can claim that he reconstructed the relationship.
“It is a win-win situation for Putin,” said Andrei V. Kolesnikov, a political analyst at the Carnegie Moscow Center.
Mr. Putin nevertheless does face some hurdles. First and foremost, it is unclear what he has to offer in exchange for American cooperation — other than collaboration in Syria and great sympathy for Mr. Trump’s plight at the hands of what Russia refers to as the American “deep state,” including the news media.
There is some speculation that Mr. Trump may be glibly walking into a trap where he will be played by the Russian leader. On the American side, Mr. Trump’s national security adviser, Lt. Gen. H. R. McMaster, said last week that there was “no specific agenda — it’s really going to be whatever the president wants to talk about.”
In contrast, Mr. Putin will surely show up with finely honed talking points aimed at forging closer cooperation and reaffirming Russia’s old Soviet role as the equal of the United States in umpiring global affairs.
“Putin will try to exploit that advantage,” said Vladimir Frolov, a prominent columnist who writes frequently on foreign policy. Mr. Putin has made it his mission to curb what he considers the dangerous impulse of all American presidents, including Mr. Trump, to interfere globally without consulting other powers.
Some in the United States, and in the West in general, view Mr. Putin with new distrust given the sense that Russia has abandoned cooperation in favor of actively working to undermine Western alliances and open, democratic systems.
Yet, Mr. Trump has shown little stomach for condemning Russia, and both presidents will most likely want to avoid as much as possible the topic of Russian meddling in last year’s election.
The Kremlin is aware that Trump critics will be watching for further signs that the American leader is soft on Russia. “Trump is being accused of cooperating with Russia, so if he makes any concessions to Moscow, these accusations will gain strength,” said Aleksei Makarkin, deputy head of the Center for Political Technologies, a Moscow think tank.
Mr. Putin has repeatedly denied any meddling, and Russia habitually blames endemic “Russophobia” for preventing Mr. Trump from being himself. That is how Moscow explains any American action seen as hostile, ranging from more aggressive military attacks in Syria to congressional efforts to buttress economic sanctions first prompted by the Ukraine crisis.
The Kremlin has watched, chagrined, as the Trump administration has rolled back various positions stated during the campaign — his questioning of the viability of NATO, for example, or his expressions of sympathy for the Russian position on Crimea.
“The Kremlin is astonished that the president cannot behave like a real president, like ours, so what can they do in this situation?” Mr. Kolesnikov asked.
Commentary in the official Russian news media suggested that Moscow was baffled by the lack of a confirmed agenda, while various senior officials and the Kremlin press service have listed possible talking points that cover virtually every major international issue.
Syria, where there has already been a measure of uneasy military coordination, is of “particular importance,” according to the Kremlin list.
Asked last month about possible outcomes from meeting Mr. Trump, Mr. Putin said, “On the Syrian problem and the Middle East in general, it is clear to all that no progress will be made without joint constructive work.”
Cooperation from Washington on Russia’s plan to create “deconfliction zones” inside Syria would go a long way toward reviving Russia’s role as a key power in the Middle East. While both leaders have expressed an interest in working together on counterterrorism, the United States still wants to see President Bashar al-Assad step down.
Another main item on the Russian agenda will be what it lumps together as “strategic stability,” including nuclear weapons. Russia wants the United States to remove the new missile defense shield based in Romania and Poland. In return, analysts said, Mr. Putin might respond to accusations about a new Russian missile that the United States says violates the historic 1987 treaty on limiting intermediate-range nuclear weapons.
Economic sanctions applied after the Ukraine crisis could come up, since Russia is struggling to revive its economy in the face of low oil prices and an uneven investment climate. In terms of Ukraine itself, Dmitri S. Peskov, Mr. Putin’s spokesman, said on Wednesday that the meeting would be too short to discuss Ukraine with the needed detail.
On Tuesday, Russia and China announced a joint effort to address the North Korea crisis, with the first step an agreement by the United States and South Korea to freeze military maneuvers in exchange for Pyongyang’s freezing its nuclear missile program. Mr. Putin is deemed likely to seek Mr. Trump’s endorsement of the deal.
But that poses problems for the American military, potentially limiting its freedom of movement in the Pacific and possibly eroding the American-South Korean deterrent.
Russia has also been publicly grinding its teeth over the loss of its two American diplomatic dachas, a penalty imposed by the Obama administration for Russia’s election meddling.
In the absence of any clearly achievable goal, Moscow has been playing down expectations, with the state news media saying just an agreement to meet again would be good enough. Yuri Ushakov, the presidential foreign policy adviser, told reporters on Tuesday that “first contact is very important.”
Aside from four telephone calls between the two presidents since Mr. Trump’s election victory, there have been minimal talks between the two governments.
Mr. Trump infamously met with Sergey V. Lavrov, the Russian foreign minister, in the Oval Office. After Secretary of State Rex W. Tillerson visited the Kremlin in April, the two sides set up a working group to try to iron out some differences. In June, after just one meeting, Russia suspended the work because of new economic sanctions.
Ultimately, a lot will ride on the chemistry between the two men, and much like any elements mingling in the same test tube for the first time, the reaction is unpredictable.
In the best case for the Kremlin, the two will get along swimmingly: Mr. Trump will be as admiring of Mr. Putin in the flesh as he was on the campaign trail, and he will emerge to treat Russia as his new best friend.
There is also the outside chance of a train wreck, with one of the prickly men somehow insulting the other and pushing already bad relations off the rails, hardening differences and prompting Twitter salvos. (Mr. Putin doesn’t tweet but his bots do.)
The Kremlin is betting on the positive, hoping that personal chemistry can slice through the problems. “They hope to sway the policy deliberations with direct contact,” said Mr. Frolov, the columnist.
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