Witnessess say that Tskhinvali is in ruins after heavy shelling by Georgian forces, and that people are fleeing across the border.
Meanwhile, Russia has started bombarding the Georgian-controlled section of Abkhazia, according to Georgia's public television.
"Russian aviation is currently bombing the villages of Sakeni and Lower Kvapchara in Upper Abkhazia," the television channel said on Saturday, referring to areas on the edge of Abkhazia.
Russian sources are reporting that Abkhaz separatist jets are bombing the Kodori gorge.
Abkhazia is the second of Georgia's two regions where separatists enjoy strong Russian backing.
With the violence escalating, Mikheil Saakashvili, the Georgian president, sought and got on Saturday parliament's approval for a "state of war" decree, valid for 15 days.
Russian tanks and troops began to pour into South Ossetia on Friday after Georgia launched a surprise offensive in a bid to reassert its control over it.
Attempts had begun the previous day at the United Nations to avert a full-scale war.
But the Security Council has been struggling to agree on a statement, with envoys from Russia and Georgia trading bitter accusations.
Envoys from the US, EU and Organisation of Security and Co-operation in Europe (OSCE) were being deployed to Georgia to seek an end to the fighting.
John Negroponte, the US deputy secretary of state, summoned Alexander Darchiyev, the Russian charge d'affaires, to the state department to press Moscow to cease military operations in Georgia.
Sergey Lavrov, Russia's foreign minister, has said at least 1,500 people have been killed in the South Ossetia conflict, and that the toll is increasing.
The Russian Interfax news agency quoted Irina Gagloyeva, a separatist South Ossetian spokeswoman, as saying: "According to our figures, around 1,600 people have died [in Tskhinvali].
"We are treating about 90 injured people in Tskhinvali hospital ... The hospital is under constant fire."
Moscow began to transport on Saturday South Ossetian refugees - whom it considers as its own citizens - into the neighbouring Russian province of North Ossetia.
Medical teams are waiting at the border to move in and help the injured, and to retrieve the dead.
Georgia under attack
As the fighting spread into Georgia proper, a military base southeast of the capital Tbilisi took a pounding from Russian jets.
A Georgian official said three soldiers died in the attack and five were wounded.
Shelling is also echoing around the city of Gori, south of the boundary between Georgia and South Ossetia and about 30km from the war front.
|Tskhinvali's main hospital has reportedly stopped functioning [Reuters]
Al Jazeera's Jonah Hull, reporting from Gori, said the city was under aerial attack from Russian jets.
He said Georgian civilians are dying as a result of the assault.
"This is the staging post for the Georgian military heading towards the front. This morning, we were talking to and filming a number of very fresh-faced-looking Georgian recruits called up as part of Saakashvili's full mobilisation of the military on Friday ... they looked relaxed they looked calm," Hull said.
"But all of a sudden the sound of a warplane was heard overhead, and a huge explosion not too far away ... they scattered like flies ... they didn't know what to do ... these were not hardened troops by any manner or means.
"Subsequently there were more explosions around the city ... cars driving in all directions carrying the injured ... all sorts of cars ... military, civilian and ambulances."
"We are told at this point that the targets of those attacks are military bases outside the city, but I am getting reports from witnesses and civilians that villages have also been hit.
Elsewhere in Georgia, in the port of Poti, Russian fighter jets hit container tankers and a shipbuilding plant, the Reuters news agency said quoting the country's deputy economic development minister.
Russian aerial bombardment has destroyed Poti, Georgia's foreign ministry said in a statement on Saturday.
| South Ossetians have been streaming into Russia to escape the fighting [EPA]
"Russia completely devastated the port of Poti on the Black Sea, which is a key port for the transport of energy sources from the Caspian Sea and is close to the Baku-Supsa pipeline and the Supsa oil terminal," the statement said.
Dmitry Mevedev, the Russian president, has defended Moscow's response to Georgia's military action in South Ossetia.
"Peaceful people are dying - women, children and the elderly. The majority of them are citizens of the Russian Federation. In accordance with the constitution and laws of this country, I am, as the president, obliged to defend the lives and dignity of our people, where ever they may be," he said in a TV address.
In a related development, the Georgian military commander said on Saturday that his country will recall all of its 2,000 soldiers from Iraq to join the fighting at home.
Colonel Bondo Maisuradze told The Associated Press news agency that all his troops would be leaving.
A US military spokesman said the departure of the Georgian contingent - the third largest contributor to international forces after the US and Britain - will have "some impact" in the near term but no significant long-term effect on Iraq's security.
The Georgians have asked the US to provide transportation, and a US spokesman said all options are being considered.