Sanders also claimed that Russian interference in the U.S. election "didn't come up" during Trump's call with Putin, nor was discussed the poisoning in the UK.
A USA administration official confirmed to Reuters that the call had taken place, without elaborating.
"I think probably well be seeing President Putin in the not-too-distant future", he said.
When asked if Russia's election was free and fair, White House spokesperson Sarah Sanders responded: "We don't get to dictate how other countries operate".
"The two leaders discussed the state of bilateral relations and resolved to continue dialogue about mutual national security priorities and challenges", said a statement from the White House.
In their phone call, the two leaders also discussed the importance of denuclearizing North Korea.
Trump, who initiated the call, opened it with the congratulations for Putin, one person familiar with the conversation said.
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Earlier this month, Trump issued a rare rebuke of Putin after the Russian leader announced new, supposedly "invincible" nuclear weapons during an annual address to the nation.
Putin won a landslide victory in Sunday's presidential election, extending his rule over the world's largest country for another six years at a time when his ties with the West are on a hostile trajectory.
"Satisfaction has been expressed with a certain decrease in tensions around the Korean peninsula", the Kremlin said.
No details were released about the timing or location of a possible meeting, which would be their third since Trump took office in January 2017.
Sanders told reporters that Trump also didn't raise the issues of election meddling or Russia's allegedly tainted voting process.
Trump's administration last week accused Russia of hacking into America's energy grid and approved the first sanctions on Russian entities and individuals for alleged meddling in the 2016 us election.
Trump continues to grapple with the shadow of the ongoing investigation into whether his campaign colluded with Russian officials during the 2016 election.