President Bashar al-Assad's forces and fighters from the Lebanese group Hezbollah launched a fierce onslaught on rebel-held districts of Homs on June 28.
"According to information just received, the al Khaldiya neighborhood has been experiencing heavy shelling since the early hours of this morning. These attacks are now affecting all of Old Homs district," said UN spokesman Farhan Haq.
UN Human Rights Commissioner Navi Pillay is "extremely concerned" about the impact of the government offensive, Haq added.
The Syrian Observatory for Human Rights said government and rebel forces were fighting on the outskirts of Khaldiya, which is gearing up to become a new landmark battle in the 27 month old Syrian war.
UN leader Ban Ki-moon has said he fears for the "trapped" civilians and called for them to be let out. But Security Council efforts to back the call for access hit deadlock.
Britain's UN ambassador Mark Lyall Grant said on his Twitter account it was "very disappointing" that a proposed statement on humanitarian access to civilians in Homs "has been blocked."
Diplomats said that Russia, Assad's major international ally, held up versions of a statement under negotiation all this week to demand that the Syrian government allow "immediate" access to Homs.
Russia similarly blocked a Security Council call last month for access to rebel held Qusayr until government forces and their Hezbollah allies had taken the key town.
Australia sent a message to the other 14 members of the Security Council on Friday expressing "disappointment" that no agreement had been reached and effectively ending negotiations, diplomats said.
Russia said it has proposed an alternative statement which called for immediate access to Homs and the towns of Nubul and Zahra, Shiite Muslim enclaves near the commercial city of Aleppo.
The Russian statement said civilians should be allowed to leave all of the towns.
"We regret that our factual proposals on the draft press statement introduced by Australia and Luxembourg have been completely ignored," a Russian spokesman told AFP.
"More than that, the text circulated yesterday has become even more imbalanced. It is based on double standards and has little to do with humanitarian issues."
Russia also highlighted a Syrian government call to the International Committee of the Red Cross to help evacuate civilians from Homs.
The spokesman said the civilians in Homs are "held by terrorist groups there as a human shield."
He added that armed opposition groups "are openly threatening Nubul's and Zahra's populations with carnage."
Russia and China used their powers as permanent council members to veto three resolutions which sought to increase pressure on Assad over the conflict.
Western diplomats said the current impasse was a new sign that it would be very difficult to secure an international agreement on the future of Syria.