But the motions, which also target 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, in a thinly veiled reference to Yingluck's brother, ousted former premier Thaksin Shinawatra.
Yingluck, who is accused by her rivals of being a puppet for her fugitive brother, told reporters 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 Sunday they had freed 137 of the 138 protesters detained for breaking a special security law invoked to deal with the unrest. The driver of the truck was retained in custody for further investigation.
National police spokesman Piya Utayo said security officials would propose lifting the special law, the Internal Security Act (ISA), on Monday subject to cabinet approval.
Politically turbulent Thailand has been rocked by a series of sometimes violent rival street protests in recent years.
Two months of mass protests against the previous government in 2010 by "Red Shirt" Thaksin supporters sparked a deadly military crackdown that left about 90 people dead and nearly 1,900 wounded.
Thaksin was toppled by royalist generals in a coup in 2006 and lives overseas to avoid a jail sentence imposed in his absence for corruption charges that he contends are politically motivated.