UPDATE: The protests have now entered their fifth straight day.
Al Jazeera reports on Prime Minister Emile Boc's reaction:
"We have achieved stability but we cannot harvest the fruits immediately," Boc said in his first speech since the protests began.
"My message is clear: violence will not be tolerated, peaceful protests are legitimate. Street violence can do us much harm and can hamper prospects for economic growth."
Boc's message came as more than 1,000 people braved freezing temperatures to rally in central Bucharest on Monday, chanting "Freedom" and waving banners that read: "Hunger and poverty have gripped Romania".
Smaller protests also took place in nearly 12 other Romanian cities.
Agencies are reporting that Romania has faced four straight days of anti-austerity protests leaving at least a dozen people injured.
The protests began on Thursday when Deputy Health Minister Raed Arafat resigned in opposition to President Traian Basescu's plans for privatizing health care.
Facing public pressure, Basescu decided to scrap the reforms Friday, saying he made the decision after realizing that a majority of those in the medical system opposed the change.
"The hospitals don't want the change, the (doctors) don't want the change and neither does the emergency health care system," Basescu said.
The health care reform was the catalyst for the outbreak of protests, the BBC reports:
But the protests have since widened to include general discontent with the government's policies.
More from CNN:
Some of the hundreds who showed up at the square on Sunday demanded justice and blamed the government and austerity measures for their poor living standards.
"We have no financial security. My husband and I are retired but we are sharing our modest income with our children because they are jobless," said Rodica Ganea, who described being asked during hospital visits to pay for "medicines, syringes, bandages, everything."
"I can't afford it," Ganea said. Another woman, 64-year-old Marilena Salan, described similar circumstances.
"My kids are university graduates but they are jobless," Salan said. "They are forced to break up their families, leave their kids home and go abroad to work. My nephews are growing up without their parents. This is unacceptable."
Reuters reports on the continuation of anti-austerity protests:
"Compared to the rest of Europe, the protests we have seen here were very small, they are not a proper instrument yet," said Cristian Patrasconiu, a political commentator. "But I do expect them to continue...This is a wave that has yet to break."
The Associated Press has video: