Yemen's rebels fired rockets and mortars into Saudi Arabia on Tuesday, killing at least three people and purportedly capturing five soldiers in an attack showing the insurgents' ability to launch assaults despite weeks of Saudi-led airstrikes targeting them.

Saudi Arabia's national airline cancelled flights into the border area of Najran as schools closed early amid the attack, the first by the rebels, known as Houthis, to target a civilian area in the kingdom since the start of the airstrikes late March.

Meanwhile, hundreds of families fled the southern Yemeni city of Aden after the Houthis advanced into their neighbourhoods, firing indiscriminately as they took over surrounding, towering mountains.

In the Saudi area of Najran, the Houthi shelling killed two Saudi civilians and damaged buildings, Yemeni tribal leaders said.

The official Saudi Press Agency carried an Interior Ministry statement saying three people had been killed, though it did not specify if they were all civilians.

The national airline, Saudia, said flights to and from the area would be suspended until further notice, without elaborating. It is the only carrier flying to Najran. Saudi state television reported local schools closed early and aired footage showing cars burnt, smoldering houses and debris covering nearby roads.

The tribal leaders, who spoke on condition of anonymity for fear of reprisals, also said the Houthis captured five Saudi soldiers in unclear circumstances.

Saudi Brig Gen. Ahmed Asiri said that Saudi-led coalition forces continue to respond to the Houthi attack.

"This attack by the militias shows their aim is to attack the livelihood of Saudi citizens," Asiri said during a call-in interview to Saudi state television. He described the situation in Najran as stable late Tuesday night.

Asiri did not offer any details about the alleged abduction of the soldiers. Saudi Apache attack helicopters also attacked Houthis near the border, said another military official, who spoke on condition of anonymity as he wasn't authorized to brief journalists.

Last week, three Saudi troops and dozens of rebels were killed in the fighting there.

The assault Tuesday underscored how the Iranian-allied Houthis are still capable of launching major operations despite more than a month of Saudi-led airstrikes targeting them and their allies — military units loyal to former president Ali Abdullah Saleh.

The Saudi-led coalition began bombing the Houthi rebels and their allies on March 26 in support of exiled President Abed Rabbo Mansour Hadi's embattled government. The airstrikes and fighting on the ground have killed hundreds and displaced at least 300,000 Yemenis.

The UN human rights office says at least 646 civilians have been killed in the conflict in Yemen since the airstrikes began, including 50 women and 131 children, the spokesman for the UN secretary-general, Stephane Dujarric, said Tuesday.

In Aden, residents said that Houthis advanced into a large section of the city's Tawahi district, forcing hundreds of families to flee to safer areas using boats. The residents said they had been trapped inside their homes for weeks.

Mona Abdel-Maged, among residents of the area reached by telephone, said a mortar shell had killed her husband, then a second shell killed six men trying to pull his body from the rubble.

"After burying the dead, we would still find torn limbs and body parts in the streets. So we go back and bury them," she said.

Mona Mohsen, one of the residents, said panic and the sound of gunfire sent people rushing into the streets.

Aden, which Hadi had declared as a temporary capital before fleeing for Saudi Arabia, is one of the main battlegrounds in a war that the UN and other aid agencies warn is pushing the impoverished nation into a humanitarian disaster.