Tillerson conceded the two world powers had "sharp differences" that have obstructed cooperation but voiced optimism that their talks could narrow those differences.
Trump has praised China for its decision to abstain from voting on the United Nations resolution, terming it an honour for the US. He also said that Putin had agreed to reactivate a U.S.
U.S. President Donald Trump said Wednesday that the relations between the United States and Russian Federation "may be at an all-time low".
"This is obviously the subject where our views differ", Lavrov retorted, adding, "Russia is not seeking to cover up for anyone in the chemical weapon incident", he added.
The US launched 59 cruise missiles on Shayrat airfield and nearby military infrastructure controlled by Syrian regime leader Bashar al Assad last Thursday to retaliate against the chemical weapons attack, that killed over 80 people, many of them children. Russian Federation wants an worldwide investigation of the chemical attack, Lavrov told reporters in Moscow, but the resolution offered by the USA and its allies was aimed "more at legitimizing the arguments against Damascus". Russian Federation made it clear it was unwilling to roll back its strategic alliance with Syrian President Bashar al-Assad.
While the Obama Administration of the last few years was every bit as hostile toward Russian Federation as the Trump Administration is, they never presented themselves as anything but hostile.
A UN Security Council resolution condemning the Syrian government for the alleged gas attack in the country's Idlib province has been vetoed by Russian Federation as a permanent member of the Security Council.
But the underlying tensions between the former Cold War foes never went away and last week s chemical attack has left ties once again in crisis.
The United States, Britain and France have pointed a finger at the Syrian government saying their experts have found that nerve agents were used in the April 4 attack. U.S. Ambassador Nikki Haley in a speech delivered to the United Nations called out Russian Federation for its support of Assad.
"Right now, we're not getting along with Russia at all - we may be at an all-time low in terms of our relationship with Russia", Trump said alongside NATO Secretary-General Jens Stoltenberg at the White House on April 12. Russian Federation has seen the same pictures that we all saw just days ago in this chamber. It's not clear to anyone at this point, with even top Russian officials responding to a week of conflicting statements by saying the U.S. stance is a "mystery". She also excoriated the United Nations for essentially standing by and taking no action to prevent the continued slaughter in Syria, stating, "Month after month we all repeat the same points in this chamber".
But Lavrov said that some progress had been made on Syria at the meeting and that a working group would be set up to examine the poor state of U.S. -Russia ties.
Only weeks ago, it appeared that Trump, who praised Putin throughout the US election campaign, was poised for a potentially historic rapprochement with Russian Federation.
Members had been asked to vote on the "imposition of sanctions on entities and individuals deemed to have been involved in the production or use of chemical weapons in Syria".
China typically sides with Russian Federation in the Security Council, including in opposing USA -backed measures to punish Syria for its use of chemical weapons.