It was Trump's first phone conversation with the Russian President since his inauguration last week, and one whose outcome will be closely studied.
CNN's Matthew Chance in Moscow said a Kremlin summary of the phone call talked about stabilizing the relationship between the two nations and several other subjects. Some of the other issues included restoring trade ties, international terrorism, the situations in Ukraine and the Korean Peninsula, and the coordination of military action against ISIS and other terrorist groups in Syria.
The Kremlin call summary didn't specifically mention US sanctions against Russia. It said restoration of mutually beneficial economic ties "could further stimulate progressive and stable development of bilateral relations," according to a CNN translation of the Russian statement.
The White House called the one-hour chat a significant start to improving a relationship "in need of repair."
Both Trump and Putin said before the call that they would like to see warmer ties between their two nations. However, relations between Trump and his team and Russia have been under scrutiny following allegations that Moscow meddled in the US election last year.
Speaking Friday at his first White House news conference
, Trump indicated a willingness to work with Moscow.
But he said it was "too early" to discuss removing sanctions that his predecessor, President Barack Obama, imposed on Russia.
"We're looking to have a great relationship with all countries," Trump said. "If we can have a great relationship with Russia and China and all countries, I'm all for that."
Friday night, however, a senior administration official said the current plan was not to lift the Russian sanctions.
The Kremlin had sought to lower expectations, suggesting Putin was calling as a matter of protocol to congratulate the US leader on his inauguration.
But there is excitement in Russia about a possible detente between Washington and Moscow under the Trump administration.
Besides imposing the Russian sanctions, Obama earlier this month expelled 35 Russian diplomats from the United States over alleged Russian interference in the 2016 election.
Flurry of calls
Before speaking with Putin, Trump held a call with Merkel and spoke to Japanese Prime Minister Shinzo Abe, a key ally in Asia.
The 45-minute phone call between Trump and Abe included a discussion of the threat posed by North Korea, and both leaders agreed to speak face to face in Washington on February 10.
Abe and Trump also discussed the significance of Defense Secretary James Mattis' upcoming visit to Asia, according to the White House.
Later Saturday, Trump was to speak with French President François Hollande and Australian Prime Minister Malcolm Turnbull.
Trump's calls with Abe and Turnbull come days after he signed an executive order withdrawing the United States from the Trans-Pacific Partnership
, or TPP, a massive trade deal negotiated by the Obama administration that Congress had not yet ratified
. Both Abe and Turnbull supported TPP.
The call between Trump and Abe did not include a discussion on a replacement for the TPP, a high-ranking Japanese government official told reporters.
The flurry of telephone diplomacy comes a day after Trump received his first foreign leader at the White House, UK Prime Minister Theresa May, who announced that Trump will make a state visit to the United Kingdom.
In a speech to US Republicans, May urged Trump to tread carefully
as he deals with Russia, saying: "With President Putin, my advice is to engage but beware."
Trump also spoke by phone Friday with Mexican President Enrique Peña Nieto
after a row over Trump's plans for a wall along the US-Mexico border culminated in Peña Nieto canceling a planned trip to Washington.
Fences to mend?
Trump's call with the German Chancellor was likely not the easiest of the day.
In an interview this month with The Times newspaper in London and the German publication Bild
, the US President called Merkel "by far the most important leader" in Europe -- but was critical of the welcome she has extended to refugees.
"I think she made one very catastrophic mistake and that was taking all of these illegals, you know taking all of the people from wherever they come from. And nobody even knows where they come from," Trump said in that interview.
He also appeared to undermine the European Union, currently grappling with the prospect of Britain's exit, saying: "You look at the European Union and it's Germany. Basically a vehicle for Germany. That's why I thought the UK was so smart in getting out."
Merkel, who is running for a fourth term in office later this year and faces criticism from political opponents over her refugee policy, declined to comment on Trump's remarks.
In their call Saturday, Trump and Merkel discussed NATO and other topics, officials said.
"The leaders recognized that NATO must be capable of confronting 21st-century threats and that our common defense requires appropriate investment in military capabilities to ensure all Allies are contributing their fair share to our collective security," the White House reported.
A German statement used the phrasing "common defense investment in military capabilities and a fair contribution of all allies."
Trump will attend the G20 summit in Hamburg, Germany, in July, the two statements said.
Trump may also have to build bridges with France, traditionally a close ally of the United States.
Hollande, who plans to stand down as president this spring, was outspoken at a joint news conference Friday with Merkel about the "challenges" the Trump administration poses
for Europe in terms of trade and global diplomacy.
"We of course have to speak to Donald Trump, as he was chosen by the Americans to be their president. But we have to do it with a European point of view and promote our interests and values," he said in Berlin.
The French government said Hollande referred to NATO as indispensible and also told Trump the nuclear agreement with Iran needs to be respected and fully implemented. Hollande added that the nations should be vigilant with Tehran.
The French President told the new American leader that situation in Syria requires a political solution and the involvement of the United Nations, according to the French statement.
As to the crisis in eastern Ukraine, Hollande said sanctions must stay in place until the Minsk agreement is implemented.
The White House said Trump offered condolences for the loss of life in terrorist attacks in France and discussed his desire to cooperate more on counterterrorism and security.
"The leaders also lauded our combined efforts to eliminate ISIS in Iraq and Syria," the White House statement said. It also said Trump, as in the other calls, reiterated the US committment to NATO and the importance of allies sharing costs.