Netanyahu's reported request to Putin precedes US President Donald Trump's first face-to-face meeting with Putin, at the G20 summit in Hamburg, Germany on Friday. Jordan and Israel are also part of the deal, the Associated Press reports, quoting an unnamed us official.
Meanwhile, Iranian officials are growing increasingly frustrated at the Trump administration's constant attacks on the July 2015 agreement Tehran signed with the USA and five other world powers to limit its nuclear programme in exchange for the lifting of worldwide sanctions.
According to the memorandum, the government and opposition forces will halt fighting in four zones, including the northwestern province of Idlib, the central province of Homs, the eastern Ghouta countryside of Damascus, and areas in the Daraa and Qunaitera provinces in southern Syria.
"We have already requested but have not received a reply so far", Lavrov told reporters after talks with his French counterpart, Jean-Yves Le Drian in Paris.
In March, Tillerson said the USA would set up "interim zones of stability" to help refugees return home in the next phase of the fight against Daesh and al-Qaeda in Syria and Iraq.
Both oppose the Islamic State group in Syria.
Obama wanted to limit America's involvement in Syria's civil war.
Trump tweets he's sending in federal help for Chicago's gun 'epidemic'
Meanwhile, Chicago police say crime in the city has decreased from 2016, when there were 4,331 shooting victims and 762 homicides. Roughly 40 ATF agents have already been working with local and state police on reducing gun violence in the city.
Of the agreement, he said: "I think this is our first indication of the US and Russian Federation being able to work together in Syria".
In recent weeks, Syrian troops, along with Hezbollah and other Shiite militias, have been moving to consolidate control over the area and to connect with Iranian-backed militias that are fighting to dislodge the IS from the Iraqi side of the border.
Tillerson has said Syria's future is one without Assad in power. Both the US and Russian Federation oppose the Islamic State group in Syria. "Russia is neither capable nor willing to give us what we want in Syria", Lister said.
"If our two countries work together to establish stability on the ground, it will lay a foundation for progress on the settlement of Syria's political future".
"Ultimately, this process, in our view, will lead to a resolution of Assad's status, the Syrian people should determine their country's political future through a political process" the USA official stressed.
She said a joint operation by Syrian government forces and the Russian air force quashed the last pockets of resistance.
Special units of Russian military police, equipped with light arms, will be deployed to de-escalation zones in Syria to provide safety and security there, Russia's special representative on Syria has announced. Russia's plan stipulates that "guarantors"-Russia, Turkey, and Iran for now-and agreed-upon partners on the ground should fight these irreconcilables".