According to the Reuters news service Russian President Vladimir Putin said he would be open to meet US President Donald Trump at an Arctic summit held in Finland in the future.
Putin and Niinistö are in Arkhangelsk, Russia, attending the International Arctic Forum.
Finland will begin its role as chair of the Arctic Council in May.
Putin noted that he is scheduled to meet with Trump at the G20 summit in Hamburg, Germany in July.
The Itar-Tass news agency reported that Putin said any eventual meeting with Trump must be well-prepared in advance.
Reuters later reported that Putin said that Moscow would support Trump in fighting terrorism and cooperate with the Pentagon and Central Intelligence Agency.
Leaders discuss Arctic's future
The leaders discussed more than possible meetings with Trump at the Russian summit on Thursday, however.
Both leaders stressed the need for cooperation in the Arctic region. At the same time, Putin also said there was a big economic potential in the Arctic.
Niinistö pointed out that the effects of global climate change is taking place at the fastest rate in northern regions, saying that average temperature in the Arctic has risen twice as quickly as other regions.
"If we lose the Arctic region, we will lose the whole world," Niinistö said.
After their panel discussion, Niinistö and Putin met privately, where they were scheduled to discuss various foreign and security policy issues, as well as the situation in Ukraine.
This article was revised at 16: 28 to add details on summit discussions.