He also said they "will probably get together in the not-too-distant future" to talk about the global arms race and other mutual concerns, such as the war in Syria and North Korea's development of nuclear weapons.
The official White House statement on the phone call said that the two leaders discussed "the state of bilateral relations and resolved to continue dialogue about mutual national security priorities and challenges" and the importance of "denuclearizing the Korean Peninsula".
The Kremlin said Tuesday's conversation between the two leaders had been broadly constructive and focused on overcoming problems in relations, which are at a post-Cold War low. "The two leaders confirmed the need for the United States and Russian Federation to continue our shared efforts on strategic stability". Speaking of the arms race, Trump said: "We will never allow anybody to have anything even close to what we have". Senate Majority Leader Mitch McConnell said there was a "lack of credibility in tallying the result". He said that during their hoped-for meeting the two men would likely discuss Ukraine, Syria and North Korea, among other things.
The White House said Monday that it was "not surprised by the outcome" of Sunday's presidential election in Russian Federation and that no congratulatory call was planned.
Mr. Trump's congratulatory call comes after the USA and other ally nations have condemned Russian Federation over a suspected nerve gas attack in London.
Video shows Florida deputy outside Parkland high school during rampage
Peterson, said the Broward Sheriff's Office had trained him to "seek cover and assess the situation" in cases of outdoor gun fire. When they arrive, Peterson pulls his weapon and goes forward but then retreats and takes up a position outside the building.
He said Trump had "insulted every Russian citizen who was denied the right to vote in a free and fair election to determine their country's future".
He's also pressed the Trump administration to respond aggressively to Russia's interference in the 2016 USA presidential election.
The call came after White House said on March 19 that it is "not surprised by the outcome".
Moscow and Washington are at odds over Ukraine and Syria, while US allegations that Russian Federation interfered in the USA presidential election, something Moscow denies, continue to cast a shadow over ties.
The revelation adds another layer to an emerging portrait in which Trump has repeatedly been reluctant to confront Putin amid an investigation into whether the Trump campaign colluded with Moscow to tilt the 2016 race in his favor. He has also spoken about the need to avoid another arms race, despite using his pre-election address to showcase new Russian arms.
Russian Federation denies meddling and Trump says there was no collusion.
"It's blatantly obvious that he has just an inexplicable level of support for President Putin", said Julie Smith, a European security expert who served as deputy national security adviser for former vice president Joe Biden.