The clashes turned violent after police fired tear gas to disperse protesters who were trying to block parliament to keep Somchai from delivering his first policy statement to legislators.
Protesters have accused riot police of using excessive force and say they will stage a large demonstration later in the week outside Bangkok's police headquarters.
The rally was initially planned for Monday but was postponed to pay respects to the two victims whose remains were to be cremated, protest organisers said.
|Demonstrators want Somchai to go and have vowed to continue their protests [AFP]
Referring to the violence, Somchai said expressed "regret about what happened", adding that he had ordered a fact-finding committee to investigate "what really happened" and another committee would be set up to determine compensation for families of victims.
His deputy, Chavalit Yongchaiyudh, resigned last week to take responsibility for the violence.
Somchai issued a renewed plea for reconciliation on Sunday and urged the People's Alliance for Democracy (PAD) to leave Government House which they have occupied since August.
Thailand has seen months of mounting political tensions since late May, when demonstrators from the PAD - a loose coalition of businessmen, academics and activists - launched their campaign to overthrow the elected government.
In early August PAD supporters moved to occupy the grounds of Government House, the prime minister's offices in the centre of Bangkok close to the parliament building.
The protests have virtually paralysed the government and forced Somchai to operate out of a makeshift office at Bangkok's old international airport.
The protesters' original aim had been to oust the then prime minister, Samak Sundaravej, whom they accused of being a puppet of Thaksin Shinawatra, Thailand's former leader who was removed in a 2006 military coup.
Samak was order by a court to step down last month for hosting a cooking show after taking office as prime minister.
But the demonstrators have also rejected his replacement Somchai, who is Thaksin's brother-in-law.
The mostly middle-class protesters who back the PAD say they will continue to protest as long as any party associated with Thaksin is in power.