Protesters' demands to dissolve the government within 30 days are "out of the question," Thai Prime Minister Abhisit Vejjajiva said on Sunday.

The New York Times has reported that speaking in a televised address, Abhisit said he was trying to work toward a peaceful solution to the country's political crisis, which has seen protesters known as red-shirts occupy sections of Bangkok for more than six weeks.

It was further reported that with the head of the nation's armed forces, Gen. Anupong Paochinda, sitting next to him, Abhisit accused the protesters of intimidation and said their ultimatum is "aimed at getting the attention of the foreign media."

The government could be dissolved and new elections could be held, but not as quickly as protesters are demanding, Abhisit has said.

He said, "Thirty days is out of the question. I don't think this problem can be solved within 30 days."

The Times also reported that more than 5,000 counter-demonstrators amassed in Bangkok Sunday, carrying signs indicating support for the government and the monarchy. The development introduced concern about the possibility of further violence, following the death of one person and wounding of scores of others when five grenades exploded on Thursday as the two sides confronted one another on Thursday.

The government will do whatever "is needed to bring back peace," Anupong said on Sunday

He also said, "We won't use violence, but as I've said earlier, the situation has escalated toward violence, so the military will have to adjust its measures."

They will persist in their campaign to have the government dissolved, Red-shirt protesters said in response to Abhisit's message on Sunday. (With Inputs from Agencies)