It was the second time in a week that the world's most powerful leaders have exchanged messages of praise.
Putin spoke by phone with Trump to convey his gratitude for intelligence supplied by the CIA which allowed Russia's FSB security service to break up a "terrorist cell" that was planning attacks in Russia's second city, the Kremlin said in a statement carried by Russian news agencies.
"The information received by the CIA was enough to detect, hunt down and arrest the criminals," the Kremlin said.
Putin also pledged that Russian security agencies would pass on any information received about terrorist threats to the United States and its citizens.
The FSB announced on Friday it had arrested seven members of an Islamic State group cell that had been planning a suicide bombing and "the killing of citizens" in crowded areas of Saint Petersburg on December 16.
Police confiscated a large number of explosives used to make homemade bombs, automatic rifles, munitions and extremist literature, it said.
On alert ahead of World Cup
On Tuesday, FSB chief Alexander Bortnikov said Russia was on alert for the possible return of jihadists from Syria ahead of the World Cup and the presidential election in 2018.
Russia has suffered several attacks this year, including a bombing on the Saint Petersburg metro in April that left 14 people dead.
The threat of attack has increased since Moscow's military intervention in Syria in September 2015 to support President Bashar al-Assad's regime, making Russia a priority IS target.
As many as 40,000 fighters travelled from all over the world, including Russia, to join IS in Syria after the 2014 declaration of its self-styled "caliphate" straddling Syria and Iraq.
In 2015, Russian security services estimated that 2,900 Russian citizens had joined the jihadist group, as well as several thousand Central Asians.
In a phone call on Thursday, Trump and Putin discussed the crisis over North Korea's nuclear programme, and the US leader took the unusual step of thanking his Russian opposite number for hailing the American economy.
The pair have lavished praise on each other in the past, with commentators describing their cozy relationship as a "bromance."