As of Thursday, it remained uncertain whether the planned encounter on the sidelines of the G-20 summit in Buenos Aires would happen, after Trump suggested Russia's seizure of three Ukrainian naval vessels might lead him to pull out.
Putin's spokesman on Thursday, however, said the meeting still was scheduled. Dmitry Peskov told reporters the two would meet around noon on Saturday on the summit's sidelines and that the two presidents would briefly speak before longer talks, between the U.S. and Russian delegations, that would last about an hour.
"We are expecting the two presidents to speak briefly at first, but everything is left to the discretion of the heads of state, Peskov said.
Should the meeting happen, the crisis in the Black Sea will hang over it, but the White House has shown little enthusiasm for talking about it. National Security Adviser John Bolton refused to say whether Putin and Trump would discuss the incident, and Trump has largely refrained from criticizing Putin.
Trump told The New York Post on Wednesday that he "didn't like the incident" but again did not criticize Russia, adding that there was a question as to whether the Ukrainian ships had acted properly.
That message likely was well-received by the Kremlin, which has been portraying the confrontation as a deliberate provocation by Ukraine's government. And Trump's reluctance to criticize Putin will be seen as auspicious by the Russian president, who -- despite a steadily deepening confrontation between Russia and the U.S. -- has expressed a persistent belief the two can build a rapport.
This week, Putin again told a conference he believes Trump is "positively inclined" toward Russia.
"Despite this extremely toxic context, President Donald Trump as before is persistently trying not to spoil contacts with the Kremlin. While president Vladimir Putin, from all appearances, has not lost hope to improve relations with the White House," Andrew Weiss, vice president of the Carnegie Fund, wrote in an op-ed for the Russian newspaper Vedomosti this week.
From that point of view, a meeting with Trump in itself is valuable to Putin. As at their previous meetings, their latest encounter is likely to include a heavy dose of media spectacle, and there's little reason to doubt it won't be as friendly as the previous encounters.
There are substantial issues the Kremlin is eager to discuss, and Bolton, who proposed the the G-20 meeting during a visit to Moscow in October, has indicated he's eager to reorient the relationship toward modest cooperation. Both sides have said they want to talk about Syria and North Korea, as well as other security issues.
At the top of the Kremlin's public agenda is U.S. withdrawal from the Intermediate-range Nuclear Forces, or INF treaty, a key Cold War-era arms-control agreement that Bolton informed Russia the U.S. would be exiting during his Moscow trip.
Russia has protested the U.S.'s leaving, as have European countries, warning it would undermine global arms control and knocks out one of the few areas where Russia and the U.S. can have substantial positive interaction. The Trump administration, though, has accused Russia of violating the treaty and believes it is outdated, allowing for China and other countries to freely develop missiles that the U.S. and Russia cannot.
Russian and European officials have expressed hope Trump might still be persuaded to reverse course on the treaty, but few observers in Russia believe that's likely. Instead, Putin will seek the moral high ground by defending the agreement, while trying to find out U.S. intentions outside it.
"Putin does not have any illusions about saving the treaty, which is probably already dead," Dmitry Trenin, the director of the Moscow Carnegie Center wrote in an article this month. "But he wants to be seen as the treaty's defender, and to be prepared for whatever practical steps the United States will take as a result."
Andrey Kortunov, the director general of the Russian Council of International Relations, which sometimes advises the Russian government, said opinion within it on the treaty's value was split. Many of Russia's military planners, he said, shared Bolton's belief that it unfairly tied the hands of Russia and of the U.S. in a world where China played a far bigger role.
Kortunov, who met Bolton during his trip to Moscow, told ABC News he'd been surprised by Bolton's optimism about U.S.-Russian relations, saying Trump's National Security Adviser had proposed trying to find new ways of working together.
The Kremlin, however, may be more cautious of seeming overly warm toward Trump, experts said, having learned the lessons from the blast wave of bipartisan fury that followed Helsinki, where Trump was denounced as a traitor and which seemed to harden Congress’ belief in needing to pursue its own sanctions against Russia.
The Kremlin also expressed optimism in a statement laying out its agenda for the meeting in Argentina, saying it hoped with "the U.S. midterms behind, the volatile domestic political factors will less influence" relations.
"After the experience of Helsinki, there is already an understanding that now it's necessary to do expectations management," Kortunov said.
Still, Kortunov added, with Russian meddling not particularly noted in the midterms, he thought perhaps the two would be able to avoid the subject that made the summer's summit so flammable.
"Of course," Kortunov said, "it won't be completely removed, but it removes that question that was maybe the most painful during the meeting in Helsinki."