Aid agencies warned Monday of a growing humanitarian crisis in Yemen as Saudi-led warplanes hit rebel positions for a third week and rival forces clashed.

In Riyadh, Yemen's Prime Minister Khaled Bahah was sworn in as vice president at the country's embassy in front of exiled President Abedrabbo Mansour Hadi.

And Hadi, in a New York Times op-ed, charged that Iran's "hunger for power" was behind the Yemen conflict, saying Tehran was fuelling a "campaign of horror and destruction" by the Shiite Huthi rebels.

The southern city of Aden saw the heaviest fighting overnight, with medics and military sources saying 30 people were killed in clashes.

In Daleh, farther north, 40 rebels and three pro-president fighters have been killed in clashes that have raged since Sunday, a local official said.

Three children were killed Monday when a shell hit their house in south Daleh, a southern activist said.

Saudi-led coalition warplanes pounded the rebel-held presidential complex in Aden, Hadi's last refuge before he fled to neighbouring Saudi Arabia as the air war began on March 26, residents said.

And on Monday, tribesmen seized control of army bases near Balhaf port, Yemen's only gas export terminal, after soldiers withdrew, sources said.

A booby-trapped motorbike exploded in Huta, capital of the southern province of Lahj, killing 10 Huthis, a source close to the rebels said.

The Huthis, who have joined with forces loyal to ex-president Ali Abdullah Saleh, advanced on Aden last month after seizing Sanaa last year.

After 19 days of the Saudi-led air campaign, the situation is rapidly deteriorating, particularly in Aden where humanitarian groups are struggling to deliver aid.

- 'Mass exodus' -

"Shops are closed. We have a problem of food," said Marie-Elisabeth Ingres, Yemen representative of Doctors without Borders (MSF).

Metaz al-Maisuri, an activist in Aden, said basic services had ceased and there had been a "mass exodus" from the city.

Adwaa Mubarak, a 48-year-old Aden resident, said: "We are unable to leave our houses to buy what we need because of the Huthi snipers."

UN Secretary General Ban Ki-moon warned on Sunday of a huge humanitarian crisis as "civilian casualties are mounting and public infrastructure is being destroyed".

Aid workers said Sanaa is also suffering, as air strikes target rebel positions there and supplies dwindle.

The Saudi-led coalition spokesman, Brigadier General Ahmed al-Assiri, blamed the humanitarian crisis on militias, saying they are "now using the schools, the hospitals, the stadiums in order to store their equipment".

"These militia are making it difficult for the relief teams."

Assiri warned the coalition would press ahead with its air war if needed.

"We are having 120 sorties by the Air Force each day and we have the capacity to increase the number."

Human Rights Watch urged the coalition to take "necessary steps to minimise harm to civilians" and urged an investigation into "alleged laws-of-war violations", including the bombing of a displaced persons camp last month.

HRW's UN and crisis advocacy director, Philippe Bolopion also noted that rebels were "unlawfully" deployed in densely populated areas and urged militants and the coalition to protect civilians.

- Foreigners evacuated -

Although some evacuations have taken place, the International Organization for Migration saying more than 16,000 foreign nationals are still stranded in Yemen.

Russia on Sunday said it had evacuated more than 650 people, and the IOM said it had flown a first planeload of 141 passengers out of Sanaa.

Riyadh has called on Iran to end its support for the rebels, accusing Tehran of assisting "criminal activities" in Yemen and giving the Huthis weapons and aid.

Iran has denied the allegation, and supreme leader Ayatollah Ali Khamenei has condemned the coalition's raids on Yemen as "criminal".

Hadi in his opinion piece accused the rebels of being Iran's "puppets".

"Having a hostile government in a nation bordering the Bab al-Mandab strait - the highly trafficked shipping lane leading to the Suez Canal - is in no nation's interest," he wrote.

"If the Huthis are not stopped, they are destined to become the next Hezbollah, deployed by Iran to threaten the people in the region and beyond.

"The oil shipments through the Red Sea that much of the world depends on will be in jeopardy, and Al Qaeda and other radical groups will be allowed to flourish."

On Monday hundreds of Iranians protested outside the Saudi embassy in Tehran against the air strikes.

And Riyadh has reinforced at least one border post with snipers and tanks, after three soldiers died in a mortar attack earlier in the conflict.