The Saba state news agency, controlled by the Houthi movement in charge of Sanaa, put the death toll in the Sawan district at 20 and said more than 50 people had been wounded. It said casualties included woman and children.
Warplanes also struck a military airbase near the capital.
Saba said medics had rushed to Sawan to try to rescue residents trapped under the rubble of homes.
The strikes came days after jets bombed the runway to stop an Iranian aid plane landing. Damage to the airport has stopped aid deliveries, officials said.
In the southern port city of Aden, clashes continued between the Houthi fighters and local militiamen over the control of the main airport.
At least 27 civilians and fighters from both sides were killed in the fight for the airport and in the port district of Mualla on Friday, a local militia source said. Eight Houthis were killed in an ambush by local militiamen in the central Crater district, the source said.
Residents said dozens of families had fled, braving Houthi sniper fire and checkpoints as homes were shelled and burned.
Sanad Shehab, a government employee, fled along with 15 family members to Aden from fighting in his hometown of al-Houta, the capital of Lahj province, after being without water or power for more than a month.
“Al-Houta is like a ghost town now,” he told Reuters.
Saudi Arabia believes the Shi’ite Muslim Houthi group is a proxy for its regional rival Iran, and Saudi backing for the resistance in Yemen’s mostly Sunni Muslim south has raised fears that Yemen could descend into all-out sectarian war.
The Houthis hail from Yemen’s far north and belong to the Zaydi sect of Shi’ite Islam. They swept into the capital Sanaa in September and pushed south and east, saying they were winning a revolution against Sunni militants and corrupt officials.
But their advance into the outskirts of Aden on March 25 triggered a Saudi-led air campaign to drive them back and aid local fighters.
On Thursday, dozens of Houthi fighters were killed in clashes with Saudi forces on Yemen’s northern border, Riyadh said, as air strikes and artillery fire rocked Aden in what residents said was the worst fighting in over a month of war.