However, later Friday the U.S. State Department said that there was no such agreement between both countries, while it looked to Russia to stop truce violations by the Syrian regime.
"There is no agreement to conduct joint air strikes with the Russians in Syria. What we are discussing with our Russian counterparts ... are proposals for a sustainable mechanism to better monitor and enforce the cessation of hostilities (COH)," State Department spokesman John Kirby said in a statement after Russia they stage joint air strikes on the Syrian opposition, including militant group Nusra Front, who violate the truce.Russia reserves the right to hit unilaterally those opposition forces in Syria who do not observe the ceasefire, state television showed Shoigu addressing a Defence Ministry meeting.
Russia and the United States pledged earlier this month to redouble efforts to find a solution to the Syrian conflict, which has killed more than 270,000 people and displaced millions since 2011, and extend a truce across the war-torn country.
Despite diplomatic efforts to resolve the five-year conflict, Moscow and Washington have been critical of each other's bombing campaigns in Syria.
The West has accused Moscow -- a staunch supporter of Syria's Bashar al-Assad -- of propping up the regime by targeting rebels fighting Assad in strikes it said were aimed against "terrorist" organisations.
Moscow has in turn repeatedly slammed the U.S. coalition, saying its strikes in Syria have been ineffective.
Shoigu said on Friday that Russia would reserve its right to unilaterally strike "international terrorist and illegal armed groups that have not adhered to the cessation of hostilities" starting from May 25.
President Vladimir Putin in March announced a partial withdrawal of Russian troops from Syria, saying Moscow's task had been "on the whole" completed.