In another attack in southeastern Yemen, a suspected Al-Qaeda suicide bomber killed 20 soldiers at an army checkpoint, the military said, revising an earlier toll of 10 dead.
Medics said dozens were also wounded in the Sanaa blast -- the largest in the capital since a May 2012 Qaeda attack on an army parade killed around 100 people.
The blast struck Sanaa's Al-Tahrir square as supporters of the rebels were preparing to stage a protest, rebel sources said.
A rebel source earlier said 21 people were killed in the attack. An AFP photographer saw the lifeless bodies of four children among the victims.
Witnesses said a suicide bomber detonated an explosive belt at a checkpoint at the entrance to the protest site, leaving steel balls strewn at the scene.
Supporters of the rebels, known as Huthis, gathered after the explosion chanting slogans demanding the fall of President Abdrabuh Mansur Hadi.
The president infuriated the rebels earlier this week by naming his chief of staff, Ahmed Awad bin Mubarak, as prime minister following a UN-brokered peace deal under which the insurgents would withdraw from Sanaa.
Since storming into Sanaa, the rebels have been tightening their grip on the city while also looking to expand their control eastwards to oilfields and to the strategic southwestern strait of Bab el-Mandab.
Foes of the Huthi rebels accuse them of taking orders from Shiite-dominated Iran.
The Huthis, who complain of marginalisation by the authorities in Sanaa, are concentrated in the northern highlands where Zaidi Shiites are a majority in otherwise Sunni-majority Yemen.
In addition to the Huthis swooping south from their Saada stronghold, the authorities have also had to deal with southern secessionist aspirations and a bloody campaign by Yemen's Al-Qaeda franchise.
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