The deeply tribal and impoverished Arabian Peninsula state, on the front line of the US battle against Al-Qaeda, is the scene of the latest emerging proxy struggle between Middle East powers.
An Arab coalition, led by Saudi Arabia and other Sunni-ruled Gulf monarchies, is battling to avoid having a pro-Iran regime on its doorstep, as Shiite Huthi rebels tighten the noose around Hadi's southern stronghold.
"I call for this operation to continue until this gang surrenders and withdraws from all locations it has occupied in every province," Hadi told a regional summit in the Egyptian resort of Sharm el-Sheikh.
Hadi later flew to Saudi Arabia with King Salman and did not plan to return to Yemen until "the situation settles", his Foreign Minister Riyadh Yassin said.
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Heavy strikes shook the rebel-held capital Sanaa for a third consecutive night until dawn today, residents said.
"It was an intense night of bombing and the windows shook," said a foreigner working for an international aid organisation in Sanaa.
More than 200 staff from the UN, foreign embassies and other organisations were evacuated from Sanaa today by air, aid workers said.
Saudi Arabia says more than 10 countries have joined the Arab coalition defending Hadi, who had arrived in Egypt yesterday to join allies at the weekend summit, a day after he surfaced in Riyadh.
He went into hiding earlier in the week as rebel forces bore down on his refuge in the main southern city of Aden and a warplane attacked the presidential palace.
At least 54 people have been killed and 187 wounded in three days of fighting between Shiite rebels and rival militia in Aden, a senior health official said.
The cause was not immediately clear.
The Arab summit, which opened today in the Egyptian resort of Sharm el-Sheikh, is expected to back the offensive against the rebels and approve the creation of a joint military force to tackle extremists.