The Red Cross says it has been refused permission to deliver aid to the Baba Amr district of the bombed-out Syrian city of Homs, despite earlier getting the go-ahead from the authorities.
ICRC President Jakob Kellenberger said the hold-up was "unacceptable".
The delay has given rise to opposition allegations that government forces were trying to get rid of evidence of summary killings.
Baba Amr has suffered heavy bombardment by government forces in recent weeks.
The rebel Free Syrian Army (FSA) said on Thursday it was leaving the district in a "tactical withdrawal".
UK Prime Minister David Cameron told Syria's "criminal regime" that it must face justice "for the blood that is on your hands".
He warned supporters of President Bashar Assad to turn their backs on their leader or face "a day of reckoning" for their involvement.
Speaking in Brussels, he also urged Russia and China to look hard at the suffering in Syria and reconsider their support for the Syrian government.
Host Aaron Schachter talks to Russian political analyst Dmitry Babich in Moscow, about the Russian government's position on Syria.