The information allowed Russian security services track down and detain a group of suspects who were planning bomb attack on the Kazansky Cathedral and other sites in Russia's second-biggest city.
The Kremlin said the Russian President asked his US counterpart to convey his gratitude to the CIA.
He also said Russian security agencies would continue to hand over any information they get about potential terror threats against the United States.
Russia's FSB security service said seven people were arrested and a significant amount of explosives and weapons seized.
The cell was said to be planning to carry out a suicide attack on Saturday, 16 December.
The conversation was the second phone call between the two leaders since Thursday, when the Mr Trump thanked Mr Putin for his remarks "acknowledging America's strong economic performance," according to the White House.
During the first call, they also discussed ways to work together to address North Korea's nuclear and ballistic weapons programme, the White House said.
Russian TV stations ran footage of FSB operatives outside an apartment building detaining a suspect, who was later shown confessing that he was told to prepare homemade bombs rigged with shrapnel.
The reports included footage of a metal container, which the suspects used as a laboratory for making explosives, according to the FSB.
Another video showed operatives breaking the doors and raiding an apartment used by other suspects.
Last week, the FSB said it also arrested several Isis-linked suspects in Moscow, where they allegedly were plotting a series of suicide bombings over New Year's.
In April, a suicide bombing in the St Petersburg's subway left 16 dead and wounded more than 50.
Additional reporting by Reuters