The two leaders held their first known phone discussion since last month's United States missile strikes against a Syrian government airbase soured relations between Washington and Moscow.
Trump and Putin also discussed escalating tensions in North Korea and how the two countries could help defuse the unsafe situation. The White House announced it would send a top State Department official to Russian-led talks on Syria that begin Wednesday in Kazakhstan.
The discussion between Trump and Putin also focused on Syria, about which the two presidents agreed that conflict in the country "has gone on for far too long", according to the statement. "The conversation was a very good one".
It would be the first meeting between the two since Trump's election to the presidency. The launch of 59 tomahawk missiles at a Syrian airbase was in response to an April chemical weapons attack launched by Syrian President Bashar al-Assad, a Putin ally.
Secretary of State Rex Tillerson met with Putin last month in Moscow.More news: US could distribute equipment to Syrian Kurds 'very quickly': spokesman
The call came on the same day that Trump's 2016 campaign foe, Hillary Clinton, gave her most extensive interview since the election and blamed Putin, in large part, for her loss.
"We never interfere in the political life and the political processes of other countries and we don't want anybody interfering in our political life and foreign policy processes", said Mr Putin.
Trump accused Bashar al-Assad regime of carrying out the chemical attack, while both Russian Federation and Damascus have denied the Syrian government role in the barbaric chemical weapons attack that killed 70 people.
Still, Trump has continued to express his desire for warmer relations with Russian Federation, albeit acknowledging that circumstances make the chance of improved relations much slimmer.
Merkel said Germany would take "decisive measures" if it believed there was foreign meddling in the election, adding it was well-known that "hybrid warfare plays a role in Russia's military doctrine".
Trump and Putin have a host of other issues to address as well.
Merkel told her counterpart that all sides must work towards a ceasefire in Ukraine, which would lead the European Union to lift its sanctions on Russian Federation.