But the motions, which are also targeting three other government ministers, appeared to have little chance of being passed by a legislature dominated by Yingluck's Puea Thai party and its coalition partners.
"The prime minister has failed to govern this country as promised. She allows corruption," Democrat Party opposition MP Jurin Laksanavisit said at the start of the debate, which is scheduled to last for three days.
"She also allows outside people to influence her and control her administration," he added.
Yingluck, who is accused by her rivals of being a puppet for her fugitive brother, ousted former premier Thaksin Shinawatra, said she was "confident" her government could defend itself.
Her six-party ruling coalition, formed after Puea Thai's decisive election win in June 2011, controls about three-fifths of the seats in the lower house.
The debate, which is due to be followed by a no-confidence vote on Wednesday, kicked off a day after riot police clashed with anti-government protesters in Bangkok.
Police fired tear gas and made 138 arrests after a group of demonstrators tried to force their way through a fence on the edge of the main protest site with the help of a truck.
But the estimated attendance of about 20,000 fell far short of the half a million target set by organisers, the royalist group Pitak Siam (Protecting Siam), who called the rally off early on Saturday evening.
Police said on Sunday they had freed 137 of the detained protesters without charge.
One man, who drove the truck, was charged with violating a special security law invoked by the government to cope with the protest.