* Eliasson urges Houthis and Hadi government to attend talks
* But cites "deep mistrust" between Saudis and Iran
* Warns al-Qaeda has gained ground during Yemen conflict
* U.N. in talks on ending Saudi-led blockade, opening ports (adds background, quotes)
By Stephanie Nebehay
GENEVA, Oct 15 (Reuters) - U.N. Deputy Secretary General Jan Eliasson said on Thursday he hoped peace talks to end the war in Yemen could start by the end of October despite "deep mistrust" between Saudi Arabia and Iran who back opposing sides.
Eliasson, speaking after meetings in Saudi Arabia, the United Arab Emirates and Iran, called for both Houthi fighters and the exiled Yemen government of President Abd-Rabbu Mansour Hadi to attend the U.N.-backed talks without pre-conditions.
Al-Qaeda has gained territory and influence in Yemen, which also made a "strong logic" for resuming talks on a ceasefire and a political process, mediated by U.N. envoy Ismail Ould Cheikh Ahmed, he said.
"I found both in Saudi and the UAE a desire, a will to move to the political phase as soon as possible. I asked both sides to make that case very strongly to the Hadi government," Eliasson said, referring to the Riyadh-based Yemeni government.
But both Gulf states "felt the Houthis were encouraged by the Iranians to go on with their political ambitions", he said.
Saudi Arabia led an Arab military intervention against the Houthis beginning on March 26 to restore the Yemeni government ousted by the group and fend off what it sees as the creeping influence of the Shi'ite Muslim group's main ally, Iran.
"I told you also about the deep mistrust that exists between key actors, not least Saudi and UAE on one side and Iran on the other. I need to balance possible optimism with this very serious problem that we have such a lack of trust among the different actors," Eliasson said.
"We have been disappointed before. Geneva talks started but not much came out of it," he said, referring to a round in June.
Yemen's Houthi forces fired a ballistic missile on Thursday in retaliation for attacks by a Saudi-led coalition, a source in the Iranian-allied group said, and a Houthi-linked television station said a Scud missile had been fired at a Saudi air base.
Eliasson, noting that a U.N. verification mechanism to inspect commercial ships heading to Yemen was in place, said the United Nations was in talks on ending the Saudi-led blockade of Yemen, where the humanitarian situation is "critical".
"We also are in discussion about opening other ports for access to Yemen. That process will go on even without the talks starting, but I'm sure they will be part of the talks also."
Reporting by Stephanie Nebehay; Editing by Tom Heneghan