"Our policy is consistent and it's formulated exclusively on the basis of global law and not under the impact of current opportunistic motives or false choice: 'You are with us or against us, '" Lavrov told Tillerson. "There is a low level of trust between the two countries", Tillerson said.
Both he and Lavrov said progress was made during the day of discussions and announced that a working group would be set up to examine the poor state of US-Russian ties.
Britain's U.N. Ambassador Matthew Rycroft said it was Russia's eighth veto in support of President Bashar Assad's regime and asked: "How could anyone look at the faces of lifeless children" and yet veto this resolution?
"We are mindful of seriousness of that particular interference in our elections and i'm sure Russian Federation is mindful of it as well". It is one serious enough to attract additional sanctions.
No communications that confirmed Russian involvement were intercepted, according to the official, however, he did say that it was likely due to the Russians being more careful in their communications, CNN reported.
The resolution asked the Syrian government to provide flight plans and logs of its military operations on the day of the incident and for the country to open its air bases to United Nations investigators.
The comments come as Russian Federation vetoed a motion in the United Nations to condemn a poison gas attack believed to be launched by Bashar al-Assad's forces that killed 87 people last week.
Russian Foreign Minister Sergey Lavrov said President Trump's administration has found itself under pressure from those who "want to prevent it from curing the wounds inflicted by Barack Obama's administration and are using the Russian card in internal political struggle".
"We confirmed our common intention of leading an uncompromising fight against global terrorism", Lavrov said at news conference following the talks.
Arab League urges Israel to end occupation of Palestinian territory
The agenda of the Summit was topped by the turmoil in Syria, the Palestinian-Israeli conflict and the Islamic State (IS). A photo handout by the Egyptian delegation showed the two leaders sitting next to each other in white overstuffed chairs.
The men know each other well from Tillerson's days as Exxon Mobil CEO. Putin had even honored Tillerson with a friendship award.
Secretary Tillerson: The final outcome does not provide for a role for Assad in the future governance of #Syria.
Then-candidate Donald Trump repeatedly praised Vladimir Putin during the campaign, and he suggested a rapprochement with Russian Federation was both desirable and possible.
Mr Lavrov blasted U.S. claims that it has "irrefutable evidence" of election interference. "No", Trump said. But, he added, "I see them using gas ... we have to do something".
"I would like to think that they didn't know, but certainly they could have. They were there", he said.
Still, Mr Tillerson sought to stress the positives from his meetings. -Russian ties and identify problems.
In a move that slightly softened the atmosphere, Lavrov said Putin had agreed to restore a U.S. -Russia air safety agreement covering Syria which Moscow suspended in retaliation for the U.S. missile strikes.
But such hopes appeared optimistic as the diplomats outlined their sharply diverging views on Syria.
Moscow has strenuously objected to Trump's decision to launch 59 U.S. Tomahawk missiles at a Syrian air base that the U.S. says was used to pummel civilians with nerve gas, resulting in 87 deaths.
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