The two leaders discussed the state of bilateral relations and resolved to continue dialogue about mutual national security priorities and challenges, the White House said.
An official statement by the Kremlin on Tuesday said Trump and Putin discussed the importance of working together on worldwide terrorism, limiting nuclear arms and economic cooperation.
"I had a call with President Putin and congratulated him on the victory, his electoral victory".
Trump even said he would "probably get together in the not-too-distant future" with Putin to talk about "the arms race" and "Ukraine and Syria and North Korea and various other things".
The officials said there have been inter-agency discussions involving the State Department and White House.
Putin and Trump agreed on the need to avoid an arms race and discussed "a possible high-level meeting", the Kremlin said.
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Putin was widely expected to win re-election to his fourth term as opposition leaders and monitoring groups raised accusations of voting irregularities, including ballot stuffing and voter coercion.
The Kremlin said their conversation was constructive, businesslike and focused on overcoming the accumulated problems in Russia-U.S. relations.
In short, Trump says he wants to avoid an arms race, yet is committed to huge military spending aimed at preventing other countries from approximating American military capabilities. Russian Federation has denied the allegations.
Trump also chose not to heed talking points from aides instructing him to condemn Putin about the recent poisoning of a former Russian spy in the United Kingdom with a powerful nerve agent, a case that both the British and US governments have blamed on Moscow...
U.S. Special Counsel Robert Mueller and three congressional committees are investigating the alleged Russian meddling in the election and whether associates of Trump colluded with Russia.
Sanders also said Trump did not broach the topic of Russia's meddling in the USA 2016 elections. One of the officials said that would be a "very serious step", especially given the last round of tit-for-tat expulsions, which left Russian Federation and the United States with significantly smaller diplomatic forces in each other's countries. Trump has said there was no collusion between his presidential campaign and Russians.