Akilisi Pohiva, a prominent pro-democracy campaigner, said the authorities had made a mistake in delaying reform of Tonga's semi-feudal system and they needed to act.
He said: "It is the responsibility of the king and the prime minister to call a meeting of cabinet [which] has the responsibility to settle the problem and to make sure the security and peace is restored to the country."
The government bowed to the protesters late on Thursday and agreed to new elections in 2008 in which a majority of the parliament would be elected directly by popular vote.
Under the current system, nobles and appointed MPs outnumber elected representatives.
Among the buildings damaged were the prime minister's office, the financial department, offices of power company Shoreline, which is partly owned by King George Tupou V, the town's only bank and Chinese-owned shops and businesses.
The six bodies were found in a Shoreline building.
Faaoa said: "We are waiting for DNA tests to confirm [their identities], as the bodies are beyond recognition."'
Laisenia Qarase, Fiji's prime minister and chairman of the Pacific Islands Forum, said peace in Tonga was crucial for the archipelago and the South Pacific region.
He said: "We are all shocked by the acts of violence which have taken place, particularly as they are so uncharacteristic of Tonga and the Tongan people, and we hope they are now at an end."
New Zealand and Australia have condemned the violence and said they are ready to help, but warned their nationals in Tonga to stay away from large gatherings.
Alexander Downer, Australia's foreign minister, said Australian and New Zealand troops were on standby but Tonga's government had said it did not want any foreign police or troops at this stage.
Downer said: "They think they can contain the situation themselves." Air New Zealand said it had cancelled flights to Tonga for a second day on Friday.