Trump said this as he hosted Russian Foreign Minister Sergei Lavrov at the White House, a day after he abruptly sacked FBI chief James Comey who was leading the investigation into Russia's meddling in the polls that brought him to power.
The White House said in a readout of their meeting that Trump "emphasised the need to work together to end the conflict in Syria, in particular, underscoring the need for Russia to rein in the Assad regime, Iran, and Iranian proxies."
And US-Russia ties had soured under Trump's predecessor Barack Obama over Russia's unyielding support for Syrian President Bashar al-Assad and the 2014 annexation of Crimea.
The war in Syria has forced million of refugees to flee the country, over which the US and Russia have for the first time since World War Two had flown combat missions in the same air space.
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Over the past six years, the US and Russia have sparred several times over the Syrian conflict, especially concerning Assad's fate, but have failed to manage a solution to end it.
"He also raised the possibility of broader cooperation on resolving conflicts in the Middle East and elsewhere. The president further emphasised his desire to build a better relationship between the US and Russia," the White House said.
Trump's meeting with Lavrov follows the Russia visit of Secretary of State Rex Tillerson to Moscow last month.
Later at a news conference, Lavrov told reporters that Trump and Russian President Vladimir Putin are expected to meet on the sidelines of the G-20 Summit in July.