Before the vote, protesters massed outside Parliament waving the Moldovan flag and yelling "early elections" as lawmakers met.
After the vote, their numbers swelled to thousands who massed outside the Parliament and scuffled with police officers before forcing their way in. They yelled "Cancel the vote!" and "Thieves!"
Police later pushed the protesters back but they forced their way into the legislature again. Some police officers were beaten by demonstrators, Radio Chisinau reported.
As the session got underway, lawmakers from the Socialists' Party booed, blew whistles and blocked off part of the Parliament. In the end, Filip merely announced his Cabinet.
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He later said he was committed to Moldova, an impoverished former Soviet republic of about 4 million, joining the European Union. Moldova signed a political and trade association agreement with the EU in 2014, something Russia opposed.
Parliament had to approve a government by January 29 or face being dissolved. Lawmakers dismissed the previous government in October amid corruption allegations.