Saudi-led air raids on rebels in Yemen killed at least 31 people on Tuesday, officials said, as the coalition intensified its attacks in the wake of a deadly missile strike.

At least 10 people were killed in Sanaa, where coalition warplanes targeted the police academy and the headquarters of the security services, both in the heart of the rebel-controlled capital, witnesses said.

And at least another 21 were killed in a wave of air strikes in the evening in Bayhan, a town south of Marea where 60 coalition soldiers died in the missile attack by the Shiite Huthi rebels on Friday.

Overnight strikes also targeted the Sanaa residences of Huthi leaders, witnesses said.

On Tuesday, plumes of smoke rose from the security headquarters in Sanaa while flying glass caused by blasts wounded many people near the police academy, others said.

Women and children terrified by the intensity of the explosions were seen fleeing into the streets.

Emirati aircraft took part in the raids on Sanaa, "hitting their targets with precision", said the UAE's official WAM news agency.

The rebel-controlled sabanews.net website reported 15 dead and 77 wounded in Tuesday's raids on the Yemeni capital.

Medical officials said at least seven "civilians" and three guards of leading Huthi officer Khaled al-Anduli were killed in the overnight strikes.

One of Anduli's neighbours, 43-year-old Hamid Hassan, told AFP that "one of my sons (an 18-year-old) was wounded when his bedroom windows shattered after the raid on the officer's house".

Ambulances rushed to Anduli's home where medics retrieved the bodies of victims, Hassan said, adding that the Huthi leader himself had been elsewhere at the time of the raid.

On Tuesday evening, the coalition launched a series of raids on Bayhan that killed least 21 rebel fighters, including 13 in a military base, military sources said.

The latest strikes come a day after the government announced that 10,000 Yemeni fighters are now ready as part of the "national army being prepared to liberate Sanaa and other provinces".

Gulf Arab members of the Saudi-led anti-rebel coalition have also reportedly sent thousands of heavily armed reinforcements to Yemen in the wake of Friday's missile strike.

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.

Saudi Deputy Crown Prince Mohammed bin Salman reaffirmed in a statement on the official SPA news agency that "the coalition will decisively continue its operations to defeat the rebels and those supporting them... who are attempting to undermine regional security".

In March, the coalition launched its air war against the Iran-backed rebels when President Abedrabbo Mansour Hadi fled to neighbouring Saudi Arabia after they entered his last refuge, Yemen's second city Aden.

After loyalists recaptured the southern port in July, the coalition began a ground operation which has seen the rebels pushed back from five southern provinces, although they still control Sanaa and much of the north and centre.