Yemen's embattled president has left the country's southern city of Aden, to visit Saudi Arabia and Egypt in a bid to consolidate support for the ongoing Saudi-led military offensive against Houthi rebels.

Abd-Rabbu Mansour Hadi arrived in the Saudi capital on Thursday evening, before heading to Sharm el-Sheikh to attend the Arab Summit on Saturday, according to Saudi state television.

Hadi's trip followed air strikes by a Saudi-led coalition on Houthi targets in the Yemeni capital Sanaa early on Thursday. Saudi state media reported that he left the city of Aden under Saudi protection.

Rights group Amnesty International said at least six children were among 25 people killed in the air strikes in the capital on Thursday. Earlier, Houthi sources said at least 18 people had been killed in bombardment.

On Thursday night, Al Jazeera received reports that air strikes targeted a reception camp of new recruits joining forces loyal to ousted President Ali Abdullah Saleh - who backs the Houthis - west of Sanaa.

Residents and security officials said the second night of air strikes throughout Yemen targeted air and ground force bases loyal to ex-president Ali Abdullah Saleh, whose forces have bolstered the Houthi advance.

Al Jazeera also learned that air strikes hit al-Anad Air Base in Aden and the Tariq Air Base in the country's third city of Taiz. Eyewitnesses also reported air strikes and loud blasts in the northern Houthi stronghold of Saada, near the Saudi border.

A spokesman of the Saudi-led coalition said the military operation against the Houthis will continue "as long as necessary." Brigadier Ahmed al-Asiri also said that "at the moment" there are no plans for the deployment of ground forces, but troops are "ready for all the circumstances".

Iranian condemnation

Houthi leader Abdel-Malek al-Houthi, in a televised speech, described the Saudi-led operation as a "despicable aggression".

Who are the Houthis? - The Houthis belong to the Zaidi community, a moderate Shia sect that makes up about a third of Yemen's population. - Their rebellion was launched in 2004 in the northern town of Saada. - Their initial demand was an end to political and economic marginalisation in the north. - Another objective was allegedly to restore the rule of Shia imams, who ruled Yemen for nearly 1,000 years. - They now say they are fighting for more rights for all Yemenis, saying people in both the north and south are being wronged by the country's rulers. - The Houthis participated in the 2011 uprising and gained political acceptance in Yemen. But soon they broke away from the rest of the political forces that deposed Ali Abdullah Saleh. - They resumed military action and have in the last six months taken control of Sanaa and other parts of Yemen. For more on the rise of the Houthis, read Mohamed Vall's 2014 blog and look at our Yemen timeline.

"What do they expect us to do, surrender, announce our defeat and act like cowards? Absolutely not. This is not how the honorable Yemeni people think. We will fight back. All 24 million Yemenis will stand united and face that despicable aggression," al-Houthi said.

Ousted president Saleh also called on the Houthis to stop attacking Aden, even as he denounced the Saudi air strikes inside his country.

Iran's Foreign Minister Mohammad Javad Zarif, speaking from Switzerland, warned that air strikes would lead only to greater loss of life .

"Military action from outside of Yemen against its territorial integrity and its people will have no other result than more bloodshed and more deaths," he told the Iranian-owned al-Alam television channel.

He also called for an "urgent dialogue" among the Yemeni factions "without external interference".

Iran has been accused of backing the Houthis in the struggle for control of Sanaa - a charge Tehran denies.

In a statement following the strikes, the White House said that the US was coordinating military and intelligence support with the Saudis but not taking part directly in the strikes.

Jeff Rathke, a US State Department spokesman, said on Thursday that the US government "understands the concerns" of Saudi is is "supportive of their effort".

Turkish President Recep Tayyip Erdogan has said that Iran had been trying to dominate the Middle East.

"It is really not possible to tolerate this. Iran has to understand," he said, adding Tehran should withdraw any forces it had in Yemen as well as from Syria and Iraq.

The European Union, however, opposed the strikes with the EU High Representative and Vice President Federica Mogherini saying the operation "dramatically worsened the already fragile situation" and "risk having serious regional consequences."