Kremlin said in a brief statement that the two presidents expressed "great concern about the extent of the new coronavirus outbreak in the world."
Trump said earlier that he would express his opposition during the call over the oil price war between Russia and Saudi Arabia that "damages" the sector of the energy in U.S.
"We don't want a dead industrial sector," Trump told Fox News.
"I never expected to say that we might need to increase oil, but we do need that," he said.
Kremlin said it was agreed to hold "Russian-American discussions on the subject between the two energy ministers."
"The possibility of close cooperation between the two countries was discussed," Kremlin statement said.
In his televised statement, Trump said Putin would use the call to push for the lifting of U.S. sanctions on Russia.
"He'll probably ask for it... He's been asking for it for two years."
Kremlin statement did not mention the sanctions, but said that "certain topics" were discussed on bilateral relations, without specifying them.
Much of the sanctions were imposed on Russia for its annexation of Ukraine's Crimea, and what U.S. investigators saw as coordinated attempts to interfere in the 2016 U.S. election in which Trump won.
On Thursday, Putin called on G20 leaders, during a video meeting, to suspend sanctions during the global Coronavirus crisis because it was a "matter of life and death."
The Russian President did not specify the countries concerned, noting that Russia was severely affected by the economic crisis caused by the epidemic and the collapse in oil prices.
The good relationship between Trump and Putin is causing controversy in the United States.