Russia and the US on Wednesday agreed to keep on fighting international terrorism and continue discussions on Syrian conflict settlement, despite turbulent bilateral relations and a string of pending disputes between the two countries.

In a news conference following talks with visiting US Secretary of State Rex Tillerson and a two-hour joint meeting with Russian President Vladimir Putin, Russian Foreign Minister Sergei Lavrov said the discussions were fruitful, underlining good prospects for future joint work.

"It has been a long day…The talks were comprehensive, frank and covered the whole spectrum of issues, which are key to our bilateral relations and interaction on the international affairs," Xinhua news agency quoted the Minister as saying.

"With all the existing problems, both objective and artificially created ones, we still have quite a few prospects for joint work. Russia is open to dialogues with the US in different areas, and not only to dialogues but also to joint actions," he added.

Echoing the Russian stance on cooperation, Tillerson said Russia and the US will continue discussions about how to find a solution to the Syrian conflict.

"Foreign Minister Lavrov and I agreed we would consider further proposals made about the way forward in Syria, including consulting with our allies and coalition members." Tillerson said in the news conference.

Tensions between Moscow and Washington have further aggravated over Syria after the US missile strike on a Syrian military airfield on Thursday, which it claims to be in response to the alleged Syrian government's chemical weapons attack last Tuesday in Khan Sheikhoun.

Earlier in an interview broadcast on Wednesday before the meeting with Tillerson, Putin said mutual trust between Russia and the US, especially on the military level, had eroded in the first few months of Trump's presidency.

Putin's view was shared by Tillerson who, on the first visit by the Trump cabinet to Russia, said ties between the two countries were at a low point marked by serious distrust.

"There is a low level of trust between our two countries. The world's two foremost nuclear powers cannot have this kind of relationship," he said in the news conference, adding that Moscow and Washington had agreed to establish a working group to identify problems and improve bilateral relations.

With a shared willingness to mend the battered ties, Russia and the US agreed on Wednesday to work together on an investigation of the Syrian chemical weapons attack, although the divergence in their stances have not changed much.

Tillerson reiterated Washington is "quite confident" that the recent chemical attack was planned and executed by Syrian government forces, which involved chlorine bombs and other chemical weapons on more than 50 occasions.

Calling for an "objective and unbiased probe" into the chemical attack in Syria, Lavrov said Russia has no intention to shield anyone responsible for the incident and repeated Russia's view that the Syrian government was not responsible for the attack.

Russia vetoed a UN resolution demanding the Syrian government cooperate with an investigation of the suspected chemical attack, saying that Moscow had consistently expressed its "categorical disagreement" with the draft resolution, which led to further criticism from the West including the US.

"The international community has spoken. Russia now has a lot to prove," US Ambassador Nikki Haley said