The body "urged the immediate implementation" of a February resolution to improve humanitarian access in the country, said Joy Ogwu, Nigeria's ambassador, who is serving as the council's current president.
She said council members also stand behind a call made by UN-Arab League envoy Lakhdar Brahimi earlier in the day to resume negotiations to end the siege.
Syrian troops and pro-regime militiamen fought their way into rebel-held neighbourhoods of the central city of Homs on Tuesday after besieging them for nearly two years.
"Civilians trapped are in real danger of being killed in the latest assault by the Syrian regime on Homs," said Britain's UN ambassador Mark Lyall Grant.
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He added that France and Britain had proposed a draft formal declaration by the council to call for Syrian government forces to lift the siege, but the council had failed to adopt it.
French ambassador Gerard Araud said that Russia, the key ally of Damascus, blocked the draft statement, despite Moscow's support for the February resolution which called for the lifting of sieges in multiple cities including Homs.
"It is imperative that those who want to leave Homs are able to do so quickly and safely," she added.
Syrian ambassador Bachar Jaafari told reporters that only 170 civilians were trapped in Homs, alongside thousands of terrorists -- the regime's term for rebels. He said the civilians refused to leave.