The Huthis, who are fighting forces loyal to Hadi and have seized large parts of the country including the capital, want talks to be held in Yemen and are staying away from the meeting of about 400 delegates in Riyadh.
The Huthis have long complained of marginalisation and fought six wars with the central government between 2004 and 2010, before launching a sweeping advance from their northern stronghold last year.
Their southward push forced Hadi to flee to Riyadh and prompted a Saudi-led coalition to launch air strikes against the Huthis, who are allied with fighters loyal to former president Ali Abdullah Saleh.
Although the Huthis are not participating, Saleh's General People's Congress party "has many of its leaders taking part", Abdulaziz al-Jaber, head of the conference's organising committee, told reporters yesterday.
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He said, however, that "we will not deal with" Saleh or others facing international sanctions.
Saleh, who led the country until 2011, has been on United Nations and US sanctions lists since November.
Jaber said the three-day meeting is "not a dialogue" but a decision-making conference.
Among the goals of the meeting is working towards a constitution which would be presented to the Yemeni people, "and to hold a referendum to put the results of the dialogue into practice," Jaber said.
"We reassure the people that restoring the state is inevitable."
About 1,600 people, many of them civilians, have been killed since late March and more than 6,200 others have been injured, while around 450,000 Yemenis are internally displaced because of the war, according to the United Nations.