At least one person killed and three injured overnight as a gunman opened fire at a group of protesters near Chamai bridge in Bangkok.
Earlier on Friday, Thailand's army chief urged both sides in the country's bitter political dispute to show restraint, but did not explicitly rule out the possibility of a coup.
Thailand has been wracked by two months of political tensions and occasionally violent street protests pitting the government of Prime Minister Yingluck Shinawatra against protesters seeking to oust her.
The army has staged 11 successful coups in the country's history, so its intentions are being watched carefully.
"That door is neither open nor closed," the army chief, General Prayuth Chan-ocha, said on Friday in response to questions from reporters as to whether military intervention was likely.
"It will be determined by the situation."
Prayuth also reiterated a request that people stop asking the army to take sides in the dispute.
"Please don't bring the army into the centre of this conflict," he said.
The protesters have been eager for the army to intervene in the crisis.
Late last month, they forced their way onto the grounds of army headquarters to deliver a letter asking the military to support their campaign to topple Yingluck.
The protesters stopped short of calling for a coup, but urged military leaders to "take a stand" in the political crisis. Prayuth responded by insisting that the army would not take sides.
On Thursday, the protesters, who are seeking to disrupt elections scheduled for February 2, battled with police in clashes that left two people dead and moe than 140 injured. Thirty of the injured remained hospitalised on Friday.
As Thursday's violence unfolded, Thailand's election commission called for a delay in the polls, a blow to Yingluck. The government rejected the call.
Deputy Prime Minister Surapong Tovichakchaikul said on Friday that he would ask the military to provide security for the elections.
Prayuth said the army had shown "red traffic lights to both sides, so things will calm down," and called for an end to street violence.
"You ask, 'Who wins?' Who wins?' No one," he said.
Police have made no move to arrest the protest movement's ringleader, Suthep Thaugsuban, who is demanding the country be led by an unelected council until reforms can be implemented.