Protesters have been trying since November to oust Prime Minister Yingluck Shinawatra, whom they see as a stand-in for her brother, Thaksin, the self-exiled former premier who clashed with the establishment and was ousted in a 2006 coup.
Ms Yingluck called a general election on February 2 to try to end the demonstrations, but protesters succeeded in disrupting the vote in about a fifth of constituencies, meaning there is not yet a quorum to open parliament and install a new government.
Election Commissioner Somchai Srisutthiyakorn said: "Voting for constituencies where elections could not take place on February 2 will take place on April 27."
Protest group the People's Democratic Reform Committee wants Ms Yingluck to step aside and reforms drawn up by a "people's council".
Its members prevented voting in much of the south and Bangkok, strongholds of the opposition Democratic Party.