Diplomats said Russia's opposition to the statement proposed by council members Australia and Luxembourg was a new sign of a growing international split over the 26-month old conflict.
The statement, obtained by AFP, sought "immediate, safe and unhindered access" to Homs, where President Bashar al-Assad's forces have been joined by fighters from Lebanese group Hezbollah against rebels.
Government warplanes bombed rebel-held neighborhoods of Syria's third city today, according to Syrian activists.
Russia, Assad's key international ally, similarly blocked a UN Security Council call last month for access to rebel held Qusayr until government forces had taken the key town.
Australia and Luxembourg proposed the new statement in a bid to strengthen calls for access made by Ban and the UN Office for the Coordination of Humanitarian Affairs (OCHA).
The proposed statement expresses "grave concern about the estimated 2,500 civilians trapped in Homs."
It said rebel and government forces should allow civilians to leave Homs, and highlighted "the primary responsibility of the Syrian government in this regard."
Russia asked for a 24 hour delay when the statement was first proposed but when the latest deadline for agreement came up this morning, put a hold on the declaration by the 15-nation body.
"The Russians have asked for changes," said one UN diplomat. "What they are asking means that there is no chance we will agree anything today, even though the situation is now urgent," added a second UN diplomat, also speaking on condition of anonymity.
Russia and China have used their powers as permanent members of the Security Council to veto three western proposed resolutions which sought to increase pressure on Assad.
Russia and the United States have said they want to hold an international conference on Syria. But original plans for a meeting in May have been pushed back to at least September and some UN diplomats say they now doubt a conference can be convened.
