The protesters' numbers have dwindled from a peak of 100,000-plus a week ago but hardcore groups have remained at the frontline, fighting running battles with the police.
On Monday, many schools and offices, including the United Nations' regional headquarters located near the Government House, were closed.
The French Embassy issued one of the strongest warnings of dozens of foreign governments, urging citizens to “stay inside” to avoid the conflict on Bangkok's streets.
The French School was one of at least 60 schools closed in Bangkok on Monday.
It is located in a northeastern Bangkok neighborhood where gunshots rang out over the weekend during clashes between Yingluck's supporters and opponents.
Suthep's meeting with Yingluck on Sunday took place in the presence of top military leaders, even though he had an arrest warrant against him.
A second arrest warrant was issued Monday on charges of insurrection.
His sustained campaign has raised suggestions that he may have the backing of the military, which has long had a powerful influence over Thai politics.
The army has often stepped in during times of crisis, carrying out 18 successful or attempted coups since the 1930s.
But this time, if the army does anything, “it will be with great hesitation” because it would have no support internationally and would find it tough to install a new civilian government acceptable to all, said Thitinan, director of Chulalongkorn's Institute of Security and International Studies.
“So this is something the army wants to avoid. It has stayed on the sidelines for now. And if it does (act), I think we can look at more turmoil down the road, I am afraid,” he said.
Political instability has plagued Thailand since the military ousted Thaksin, who remains hugely popular among rural voters, in 2006.
Two years later, anti-Thaksin protesters occupied Bangkok's two airports for a week after taking over the prime minister's office for three months, and in 2010 pro-Thaksin protesters occupied downtown Bangkok for weeks in a standoff that ended with parts of the city in flames and more than 90 dead.
“I believe that no one wants to see a repeat of history, where we saw the people suffer and lose their lives,” Yingluck said.
