Late Wednesday, President Trump called Mr. Putin to offer American help in battling the infernos. Mr. Putin said that he would accept the offer if it became necessary, but that Russian agencies are now working hard to handle the crisis. Mr. Putin was criticized last week after he offered Greece help in fighting wildfires.

But the Kremlin interpreted Mr. Trump’s call as a positive gesture that could improve the embittered relations between the two countries.

“The president of Russia regards the U.S. president’s offer as a sign that it is possible that full-scale bilateral relations will be restored in the future,” the Kremlin said in a statement. It added that the two leaders had agreed to stay in contact, both over the phone and in face-to-face meetings.

Mr. Putin and Mr. Trump have been working to mend ties between their countries, which turned sour after Moscow intervened in conflicts in Ukraine and Syria.

The Russian regions of Krasnoyarsk, Irkutsk and Yakutia are currently among the worst affected by the disaster. The authorities declared a state of emergency in all of Krasnoyarsk and Irkutsk — an area the size of Western Europe, stretching from Mongolia to the Arctic Ocean. Emergencies were also declared in parts of Yakutia and another region, Buryatia.

Images published by NASA showed the smoke reaching the United States and Canada.

The head of the Russian weather forecasting agency, Rosgidromet, told Interfax that global warming would make wildfires worse.

“The situation will get worse every year because we can see how climate changes everywhere, even in Russia,” said the agency’s chief, Maksim Yakovenko.