Trump told reporters at the White House he had spoken with Putin, two days after the Russian strongman sailed to a fourth term as president, and with ties strained by the Cold War-style intrigue over the poisoning of an ex-spy in Britain.
"I had a call with President Putin and congratulated him on his electoral victory," the US leader said.
"The call had to do also with the fact that we will probably get together in the not-too-distant future," he added.
According to a Kremlin statement, the two leaders also stressed the importance of joint efforts to limit an arms race and boost economic cooperation.
"On the whole, the conversation was constructive and business-like," the Kremlin said, adding that its goal was to help the two countries "overcome the problems that had accumulated in the Russian-US relations".
Russia is under pressure from London and its allies to explain how its former double agent Sergei Skripal and his daughter were poisoned on British soil, with a nerve agent the UK says is Soviet-designed.
Moscow has denied being involved.
Although the nerve attack has topped global headlines for weeks, it did not come up during the leaders' conversation, according to both the Kremlin and White House.
"I don't believe that was discussed in today's call," White House spokeswoman Sarah Sanders said.
Neither did they address Washington's imposition last week of a new round of sanctions against Moscow designed to punish Russians responsible for attempts to interfere in the 2016 US presidential elections.
Nor did they discuss the questions that have been raised over the weekend poll in Russia.
"The focus was to talk about areas of shared interests," Sanders said.
'Sham elections'
Those shared interests, according to the Kremlin, included the crises in Ukraine and Syria, and ways of "developing practical cooperation" in various spheres including the fight against terrorism.
Pyongyang's nuclear program was on the agenda as Trump pushes forward with plans for a historic summit with North Korean leader Kim Jong Un.
"Satisfaction has been expressed with a certain decrease in tensions around the Korean peninsula," the Kremlin added.
The leaders also paid "special attention" to "working out the issue of holding a possible meeting at the highest level."
In the aftermath of an election that appears to have had significant flaws, a prominent American critic of Putin -- and of Trump himself -- offered a stinging denunciation of the US commander in chief's call.
"An American president does not lead the Free World by congratulating dictators on winning sham elections," said US Senator John McCain, who is home in Arizona battling cancer.
"And by doing so with Vladimir Putin, President Trump insulted every Russian citizen who was denied the right to vote in a free and fair election to determine their country's future."
The White House had earlier indicated that no call with Putin was planned, as the Russian leader played down talk of a rift.
On Sunday, Putin secured a landslide victory in a presidential election that saw him return to the Kremlin with a record vote share of 76.66 percent.
The Kremlin on Tuesday released a list of those who had sent congratulatory messages -- including the leaders of Greece, Germany, Iran, the Czech Republic, Finland, Syria and North Korea.
Western leaders were slow to congratulate Putin as monitors reported ballot stuffing and other alleged cases of fraud, though fewer irregularities were reported than in previous years.
Putin said Monday he would address disputes with the West but stressed that international relations were a two-way street.
"From our side, we will do all we can so that the disputes with our partners be resolved by political and diplomatic means," he said.
"It goes without saying that not everything depends on us -- as with love, both sides have to be involved, otherwise there can be no love at all."
