A Sunni Arab coalition, led by Saudi Arabia and other Gulf monarchies, is battling to avoid having a pro-Iran regime on its doorstep, as the Huthi rebels tighten the noose around Hadi's southern stronghold of Aden.
"I call for this operation to continue until this gang surrenders and withdraws from all locations it has occupied in every province," Hadi told an Arab League summit in the Egyptian resort of Sharm el-Sheikh.
"I say to Iran's puppet and whoever is with him, you are the one who destroyed Yemen with your political immaturity," Hadi said.
He later flew to Saudi Arabia with King Salman and does not plan to return to Yemen until "the situation settles", Foreign Minister Riyad Yassin said.
"The Huthis are trying to take it (Aden) by any means to impose a new reality on the ground before the summit ends," Yassin added.
Late Saturday, anti-Huthi popular committees fighters were reported to have taken full control of Aden airport with the loss of five men, and nine killed on the rebel side.
- Moscow warning -
Russia's chief negotiator in the Iranian nuclear talks said Moscow hoped that the Yemen fighting would not jeopardise the negotiations between Tehran and world powers under way in Switzerland.
"Unfortunately, we are seeing that the tragedy that is happening in this country (Yemen) is having an impact on the atmosphere of the negotiations," Moscow's deputy foreign minister Sergei Ryabkov was quoted as saying by RIA Novosti news agency.
"We hope that the situation in Yemen will not bring about a change in the position of certain participants."
As night fell on Saturday, coalition air strikes resumed for a fourth night, residents of the capital said.
More than 200 staff from the UN, foreign embassies and other organisations were evacuated by air earlier in the day, aid workers said. Pakistan said it was preparing to evacuate its citizens and diplomatic staff.
According to Saudi Arabia, more than 10 countries have joined the coalition defending Hadi.
The Western-backed leader had gone into hiding earlier in the week as rebels bore down on Aden and a warplane attacked the presidential palace there.
Hadi surfaced in Riyadh Thursday before heading to the Egypt summit.
At least 61 people have been killed and around 200 wounded in three days of fighting between Shiite rebels and anti-Huthi militia in Aden, the city's health department director Al-Kheder Lassouar said.
Fourteen charred bodies were also pulled from an arms depot in a cave near the port city after a series of massive blasts, he said.
The cause was not immediately clear, but residents had been looting the arsenal of Soviet-era weapons, apparently to defend themselves as the city slides into chaos.
The two-day Arab summit, which opened Saturday, is expected to back the offensive against the rebels and approve the creation of a joint military force to tackle extremists.
- Saudi pledge -
Egyptian President Abdel Fattah al-Sisi told fellow leaders the region faced "unprecedented" threats.
And Saudi King Salman vowed that the air strikes would continue until they bring "security" to the Yemeni people.
But UN Secretary General Ban Ki-moon urged Arab leaders to "lay down clear guidelines to peacefully resolve the crisis in Yemen".
Saudi warships evacuated dozens of foreign diplomats from Aden hours before the kingdom launched the air strikes on the advancing rebels, state television said on Saturday.
Riyadh has vowed to do "whatever it takes" to prevent Hadi's overthrow.
But experts say the Saudis will be reluctant to send in ground troops for fear of getting bogged down in a protracted conflict.
The Huthis are backed by army units loyal to former president Ali Abdullah Saleh, who stepped down in 2012 after a year-long popular uprising and is accused of supporting the rebels.
In a televised speech Saturday, Saleh urged the Arab League to help end the crisis "peacefully", saying the "problem will not be solved with strikes".
Gulf diplomats said the bombing could last up to six months, and accused Iran of providing "logistical and military support" to the rebels.
"According to estimates, there are 5,000 Iranians, (members of the pro-Tehran Lebanese movement) Hezbollah and Iraqi militia on the ground in Yemen," said one Gulf official, who did not want to be named.
It was not possible to independently verify the claim.
The Gulf officials said Riyadh and its allies had decided to intervene after satellite imagery in late January showed the movement of Scud missiles north towards the Saudi border, with the capacity to strike a large part of the kingdom's territory.
A coalition spokesman told reporters Saturday that "most" of the Huthis' missile capabilities were believed to have been destroyed in the air strikes.