* Gulf neighbours still lack formula to overcome impasse
* Aden bomb kills military official
* Thousands of anti-Saleh protesters turn out in Sanaa
(Adds GCC meeting concludes without movement on deal)
By Asma Alsharif
JEDDAH, June 14 (Reuters) - Yemen's Gulf neighbours renewed an offer on Wednesday to mediate in Yemen's bloody political crisis, but offered no formula to break a deadlock over the fate of wounded President Ali Abdullah Saleh.
Gulf states, fearful civil war may erupt on their doorstep, have tried three times in vain to broker an exit for Saleh, who is clinging to power after months of protests against his rule.
Saleh was forced to seek treatment in Saudi Arabia for injuries suffered in an attack on his palace earlier this month.
The failure of the most recent mediation bid in May kindled two weeks of fierce fighting in the capital and fanned Western and regional fears of Yemen slipping into chaos and giving al Qaeda a stronghold alongside vital oil shipping routes.
The Gulf Cooperation Council (GCC), a bloc of monarchies neighbouring Yemen, has seen Saleh back out of deals it struck to ease him from office on three occasions.
One member, Qatar, pulled out of negotiations last month after a complete breakdown of its relations with Saleh.
"With regards to Yemen it is clear that the initiative of the five GCC countries ... the latest decision to put it (the initiative) on hold is still ongoing. The Yemeni president has been invited to sign," GCC Secretary General Abdullatif al-Zayani told reporters in Jeddah after a GCC summit.
"The five countries are willing to continue in the case that all Yemeni factions request it."
Earlier, Sheikh Sadeq al-Ahmar, a leader of Yemen's powerful Hashed tribal confederation, parts of which have turned against Saleh, said Vice-President Abd-Rabbu Mansour Hadi, the acting leader, must allow a transitional government to take shape.
"Constitutionally...he must bear his responsibilities and go forward with them until the transitional period," he told the Arab satellite network Al Jazeera.
Yemen's state news agency said Saleh, who has not been seen in public since the palace attack, spoke by telephone with Saudi King Abdullah on Tuesday.
Saudi press agency SPA said that the king reiterated the kingdom's "support for a united, secure and stable Yemen".
Yemen's ambassador in London said on Saturday that he was stable and recovering from burns and shrapnel wounds, a theme repeated in state media in subsequent days.
Two members of his cabinet wounded in the attack were in a worse condition and required more surgery.
A bomb killed a military officer loyal to Saleh in Burayqa near the southern port of Aden, an official said on Tuesday.
The explosion tore through the car of Colonel Muti'a al-Sayani, a close relative of a provincial governor who is among Saleh's supporters.
Aden is swamped with refugees fleeing fighting between the Yemeni military and Islamist militants who have seized the capital of a neighbouring province -- one of the multiple conflicts that Yemen's neighbours fear could shatter the Arabian Peninsula country and embolden the country's al Qaeda wing.
A U.S.- and European-brokered effort to strike a transition agreement between Saleh's deputy and opposition parties who demand the president surrender all claims to power immediately, fell apart after the deputy refused to discuss Saleh's fate.
Yemen said on Monday it had arrested several people for trying to kill Saleh, apparently referring to the attack that wounded him. A state newspaper reporting the arrests hinted that blame would be placed on a group of opposition parties.
A ceasefire has held in Sanaa since Saleh left following the June 3 attack on his palace. Up to then, fighting between Saleh's forces and those of General Ali al-Mohsen al-Ahmar -- who defected in March -- as well as tribesmen had killed hundreds of people and put thousands to flight.
Thousands of anti-Saleh protesters filled the capital's central Siteen Street on Tuesday, demanding again that he step aside and that a transitional government be formed to take over.
Shortages of fuel, electricity and water are acute in the capital, and violence in the southern province of Abyan, whose capital Islamist gunmen seized last month, has worsened.