The United States on Monday named a dozen Syrian generals and officers accused of leading attacks on civilian targets and running torture prisons, warning they will one day face justice.

US Ambassador Samantha Power read out the names at a tense Security Council meeting on Syria, where government forces backed by Russia pressed on with an offensive as the humanitarian crisis reached alarming levels.

Nearly one million people are now living under siege, UN aid chief Stephen O'Brien said, a dramatic increase from 486,700 Syrians cut off by besiegement six months ago.

Power said many of the military commanders were involved in killing civilians with assaults on schools, hospitals and homes since the outbreak of the war in 2011.

"Today's atrocities are well-documented and the civilized world's memories are long," she said.

The ambassador listed a number of facilities where cases of torture have been documented and warned officers and prison officials that the world was watching them.

Among those named were five major generals -- Adib Salameh, Jawdat Salbi Mawas, Tahir Hamid Khalil, Jamil Hassan and Rafiq Shihadeh -- along with five brigadier generals and two colonels.

"The United States will not let those who have commanded units involved in these actions hide anonymously behind the facade of the Assad regime," she said.

The council met as Syrian and Russian warplanes pounded rebel-held parts of northern Syria while food rations were running out in east Aleppo, which has been under siege since July.

- Where are the names of terrorists ? -

Western powers have turned up the pressure on Russia over its Syria campaign after diplomatic efforts to agree on a ceasefire collapsed two months ago.

Russia in turn blames the United States for failing to convince its allies on the ground to distance themselves from the Al-Qaeda-linked Nusra Front, which has renamed itself Fatah al-Sham.

"Those behind such attacks must know that we in the international community are watching their actions, documenting their abuses and one day they will be held accountable," said Power.

"These individuals feel impunity," she said, warning that so did former Serbian leader Slobodan Milosevic and Liberian warlord Charles Taylor who eventually faced trial for war crimes.

Russian Deputy Ambassador Vladimir Safronkov accused Power of "trying to bring the whole world into a tribunal".

"Where are the names of the terrorists?" he asked. "Who is going to deal with them? Let's try not to be hypocritical."

Russia maintains that its military campaign is aimed at rooting out militants from Al-Nusra and the Islamic State group, which controls northeast Syria.

The US, French and British ambassadors walked out of the council chamber in protest as Syrian Ambassador Bashar Jaafari took the floor.

Jaafari once again argued that his government is fighting a "terrorist statelet" operating on its territory.

More than 300,000 people have died in the war that began with anti-government protests, and millions have been driven from their homes.