The protesters, who belong to the United Front for Democracy Against Dictatorship, are demanding that Abhisit Vejjajiva, the prime minister, dissolve the government and call fresh elections.
A one-week deadline set by the yellow shirts, officially known as the People's Alliance for Democracy (PAD), for an end to the crippling protests, expired with no end in sight to the tense standoff.
In Monday's other developments, an explosion occurred on Monday near the home of a senior member of one of the ruling coalition parties, injuring eight people, in Bangkok.
However, no serious violence was reported in the shopping area where at least 8,000 people were still singing and listening to speeches.
Thailand is largely split between the mainly rural poor and urban working-class red shirts, who support Thaksin Shinawatra, a former prime minister, and yellow shirts who staged their own street protests that led to a 2006 coup ousting Thaksin.
Abhisit has rejected an offer by the red shirts to disperse if elections are held in three months' time - softening earlier demands for snap polls.
Appearing on national television on Sunday alongside his army chief, Abhisit vowed to retake the sprawling protest site that has paralysed Bangkok's main retail district, but gave no indication of when a crackdown might come.
Al Jazeera's Wayne Hay, reporting from Bangkok, said the yellow shirt's action could make the situation worse.
"They [yellow shirts] could be on the streets by Monday evening ... They gave the government a week to solve the problem ... or they would take matters into their own hands and launch their own protest," he said.
"When we spoke to them a week ago, when they issued [their] demand to the government, they said they wouldn't rule out direct confrontation with the red shirts.
"Whether or not that means they will take their protesters to the streets and go near the red shirt protesters is unclear at the moment.
"There's a strong chance that they could make things a lot worse. They have a lot of support. We saw that when they took over the two airports in Bangkok [in December 2008]."
Meanwhile, the red shirts have fortified their encampment in central Bangkok amid rumours of an imminent military crackdown.
Jatuporn Prompan, a red shirt protest leader, said an appeal for supporters to turn out in force probably thwarted any crackdown.
"We had stepped up security with more guards patrolling throughout the night and many people were awake with us to make sure the army couldn't crack down," he said on Monday.
"We received intelligence it would be done this morning, but thankfully we prevented that. We will continue to fight until our victory is achieved.
"We don't want to talk to the government because there is nothing to talk about. We cannot agree and the only way is for Abhisit to dissolve the house now."
The political stalemate has rekindled fears of more unrest and a heavier toll on Southeast Asia's second-biggest economy as more retailers shut their doors and tourist numbers dwindle.