Witnesses and an AFP correspondent said targets included the police academy and the headquarters of the security services, both in the heart of the city which Shiite Huthi rebels have controlled since September last year.
Overnight strikes also targeted the Sanaa residences of Huthi leaders, witnesses said.
Medical sources said that at least seven "civilians" and three guards of a leading Huthi member were killed in the strikes.
The rebel-controlled sabanews.Net website reported that 15 people were killed and 77 wounded in Tuesday's raids.
Gulf Arab members of the Saudi-led anti-rebel coalition have also reportedly sent thousands of heavily armed reinforcements to Yemen after a Huthi missile attack killed 60 coalition soldiers on Friday.
The additional troops, mostly from Qatar and Saudi Arabia, were deployed to the battleground eastern oil province of Marib where the attack took place, the reports said.
In March, the coalition launched its air war against the rebels when President Abedrabbo Mansour Hadi fled to neighbouring Saudi Arabia after they entered his last refuge, Yemen's second city Aden.
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