Anti-government protesters want the Thai prime minister to step down from his job within 30 days, a proposal that comes as the so-called Red Shirts continue to occupy a major commercial district in Bangkok.

After holding unofficial talks with the Thai government this week, the Red Shirts said Friday that they want Thai Prime Minister Abhisit Vejjajiva to leave his job and call new elections within a month's time.

The Red Shirts claim the Abhisit-led government is illegitimate, as it seized power after court rulings ousted two pro-Thaksin Shinawatra governments. And the protesters have held their ground in the Thai capital for nearly six weeks as they push for what they want.

Thaksin, a populist leader favoured by the Red Shirts, has been living in exile to avoid a two-year prison sentence he faces for corruption.

The Red Shirt protesters said their 30-day timetable was a concession from their initial demand that Abhisit call elections immediately.

Jaran Ditthapichai, a Red Shirt leader, said that during unofficial talks the government had privately suggested that it could dissolve parliament within three months.

But the prime minister didn't respond publicly to the demand. Instead, he said the country should bind together to avoid lawlessness.

He also hinted that he would not immediately bend to the protests.

"I just want to say that I will not stay on if I don't mean to solve the problem," Abhisit said.

"Currently, I believe that I grieve as everybody does. And I intend to solve the problem."

CTV's South Asia Bureau Chief Janis Mackey Frayer said there is a sense that both sides need to give if the crisis is to be resolved.

"The government is saying that it can't risk another bloody confrontation like the one here earlier this month that saw 25 people killed," Mackey Frayer told CTV News Channel by telephone from Bangkok on Friday morning.

"Both sides would lose in a situation like that, so there is the sense that it is the perfect stalemate and both sides have to concede something."

It also appears that protesters have drawn back from their aggressive position in light of the violence that occurred in recent days -- including grenade attacks that started Thursday night.

Prinya Thewanaruemitkul, a law lecturer at Bangkok's Thammasat University, said this bodes well for a resolution.

"At least, this is better than before. Here is a chance that the crisis won't end with blood," he said.

"It might seem both sides won't compromise, but there is a path leading toward a timeframe they could mutually agree upon."

Deadly violence

The Thai government's Erawan Emergency Center reported that the late-night attacks killed one person and injured 86 others.

They took place in the area where the Red Shirts have been milling about and they struck areas where pro-government protesters had gathered.

Still, the Thai government did not directly blame the Red Shirts for the violence.

"This is the work of the terrorists that the government has always been wanting to get rid of," said Panitan Wattanayagorn, a government spokesperson, adding that it was too soon to conclude who was responsible.

Tharit Pengdit, the head of a key security agency, said anyone found to be involved in "terrorism" put themselves in a position to face the death penalty.

He urged the public to stay away from the areas where the protests are taking place.

The presence of the protesters in the central business district has shut down many banks, hotels, shopping malls and offices in the Thai capital.

The unrest is growing and Bangkok residents are growing increasingly concerned as the city remains in disorder, said Mackey Frayer.

"It's been all but paralyzed for a month and a half now," Mackey Frayer said. "People are frustrated and they are now very afraid."

All around the city, shoppers are greeted with signs reading "Sorry, closed due to political unrest."

With files from The Associated Press