Meanwhile, civilians shunned Russia's offer to quit the besieged enclave for a second day on Wednesday, as rebels and Moscow blamed each other for the humanitarian deadlock.
During this period, the route will be provided to the citizens of Eastern Ghouta to get out. UN Secretary-General Antonio Guterres described the circumstances in Eastern Ghouta as hell on Earth.
The accusations come on the third and possibly last day of a Russia-ordered "humanitarian pause" in the fighting in the area, known as eastern Ghouta, but no civilians have used the lull to leave the rebel-held suburbs.
Even as "hundreds of rockets" from the east "had reportedly fallen on Damascus" since February 18, he said, "over 580 people" had been reported killed and "well over 1,000 injured" in government air and ground strikes on Eastern Ghouta over the same period, he said.
Mr Lowcock said lorries loaded with supplies have been poised to go to 10 besieged areas, including Douma, the main town in the enclave, since Saturday.
No humanitarian convoys had reached besieged areas, he said, no government permission had been received to cross military lines, no promised medical evacuations or civilian exits had taken place, and there had been no humanitarian improvement at all. "More bombing. More fighting. We hope that you don't cooperate with the terrorists", the presenter reading from the flier said.
The US, supported by other Western nations, objected because the statement didn't reflect the resolution's demands, according to diplomats who spoke on condition of anonymity because consultations were private.
Moscow's "humanitarian pause" echoes a similar tactic employed by Russian Federation and the Syrian regime as they looked to force rebels out of second city Aleppo during a ferocious 2016 battle.
Civil defense team member carries a wounded baby rescued from a wreckage after Assad regime forces carried out airstrikes Credit Getty
"Medical and other essential services are absent and access for humanitarian workers to the city remains precariously limited because the conditions are so risky", Lowcock said.
USA representative Kelley Currie accused the regime of violating the ceasefire, while Russian ambassador Vassily Nebenzia blamed the rebels.
"According to the information received, over the 24 hours, the number of appeals from residents of Eastern Ghouta to human rights activists has increased by several times, with requests to help and assist in their evacuation from the territory controlled by militants", spokesman for Russian center for Syrian reconciliation Maj.
Last month, U.S. Secretary of State Rex Tillerson said Russian Federation was ultimately to blame for any use of chemical weapons in Syria, and accused Moscow of violating a 2013 accord with Washington on the removal of chemical weapons from Syria.
Nebenzia said what is needed above all in eastern Ghouta is "to effectively neutralize" the Nusra Front, calling for cooperation to get rid of the extremist group.
Lavrov also accused the United States and its allies of "simply exploiting baseless allegations of toxic-weapons use by Damascus as a tool of anti-Syrian political engineering". "The cessation of hostilities is for at least 30 days, every day, all day".
FILE - Russia's U.N. Ambassador Vassily Nebenzia speaks to reporters after attending a Security Council meeting, August 9, 2017, at U.N. headquarters.