The Russian president expressed his honest gratitude for such a caring attitude and the offer of help and support.
The fires cover more than 30,000 square kilometers, an area the size of Belgium, and are concentrated mainly in the vast regions of Yakutia in the north and Krasnoyarsk and Irkutsk in the east.
The two leaders agreed to continue their contacts over the phone and in face-to-face meetings, the Kremlin said.
The call between Trump and Putin comes just days before Friday's expected USA withdrawal from the 1987 Intermediate-Range Nuclear Forces (INF) Treaty with Russian Federation.
Trump has nonetheless tried to maintain a personal friendship with Putin.
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The Fed has held the interest rate steady in its prior announcements this year after raising the interest rate four times in 2018. Currently, traders are pricing in a 77 percent chance of a second quarter-percent cut during the FOMC's September meeting.
"The U.S. president offered Russian Federation cooperation in fighting forest fires in Siberia", a statement from the Kremlin, quoted by Reuters, said.
Putin did not specify what help Trump offered in battling the blaze.
'There is no reason for these massive, deadly and costly forest fires in California except that forest management is so poor, ' Trump said at the time. Climate scientists say global warming is to blame. About 3 million hectares were burning as of Wednesday, according to the country's Federal Forestry Agency. Air travel has been disrupted.
Putin made this decision after listening to a report presented by the Emergencies Minister Yevgeny Zinichev, it said.
Some 2,700 firefighters were already working to tackle the blazes, Interfax news agency reported. The ministry set up a team of ten Ilyushin Il-76 planes and ten Mil Mi-8 helicopters to help fight wildfires in the Krasnoyarsk Territory. Russian Prime Minister Dmitry Medvedev held a session in Krasnoyarsk on the situation with Siberian wildfires.
Greenpeace spokesman Grigory Kuksin said deploying army units to the forest could do more harm to the operation than good.