Abdullatif al-Zayani, the head of the Gulf Cooperation Council which tabled the plan, quit Sanaa after Saleh declined to put his name to it "as president of the republic," opposition spokesman Mohammed Qahtan said on Saturday.
"This is an essential point in the plan which we will not back down on," Qahtan told AFP.
The GCC deal proposes the formation of a government of national unity, Saleh transferring power to his vice president and an end to the deadly protests that have rocked the impoverished country since late January.
Under the accord, the Yemeni strongman would submit his resignation to parliament within 30 days, to be followed two months later by a presidential election.
However, a defiant Saleh, who has been in power for 32 years, has publicly insisted on sticking to the constitution in any transfer of power, even though his ruling party has said it accepts the GCC plan.
Zayani had gone to Sanaa to formally invite Saleh and his opponents to sign the power transfer deal, state media said ahead of what was expected to be a signing ceremony in Riyadh on Monday.
But he left the Yemeni capital empty-handed after the president refused to sign the deal himself, instead assigning one of his advisers to do so on his behalf, sources close to both sides said.
And after Zayani informed members of the Common Forum - an alliance of parliamentary opposition groups - of Saleh's position, they also refused to sign the pact unless the veteran leader does.
"We are ready to go to Riyadh, but only if Saleh signs the agreement," an official from the Common Forum said earlier.
Zayani's visit to Sanaa came a day ahead of a meeting of foreign ministers of the six-nation Gulf Cooperation Council to finalise their plan for Yemen.
However, the meeting will no longer take place.
The Yemeni leader had met with loyalists on Saturday before holding talks with the GCC chief.
Saleh "met with more than 400 members of the government, parliament and the (ruling) General People's Congress party to discuss the GCC initiative," party spokesman Tareq al-Shami told AFP.
A GPC statement then said the president "does not have to sign the agreement, which must bee signed by the GPC and the Common Forum".
It added that Saleh's adviser, Abdulkarim al-Iryani, would lead the government delegation at the signing ceremony in Riyadh.
"Saleh is ready to sign the agreement but only as head of the GPC and not as Yemen's president," GPC deputy secretary general Sultan al-Barakani had told AFP, in a concession rejected by the Common Forum.
Serviceman and civilians killed
Meanwhile, two servicemen and four civilians were killed and at least another 23 were wounded in Yemen's main southern city of Aden during a shutdown called by anti-government protesters on Saturday, officials said.
The defence ministry said an officer and a soldier were killed and two more soldiers were wounded, but gave no further details as tension mounted in the restive region.
Demonstrations calling for the veteran leader's immediate ouster have cost more than 145 lives in the past three months.
Negotiated solution would be a first
If the agreement is signed it will be the first time that a negotiated solution ends one of the many revolts that have shaken the Arab world since January.
The GCC comprises Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.
Saleh accused Qatar of a "conspiracy" and threatened to pull out of the transition deal, in an interview with Russia Today television on Friday.
"Contacts are under way for the signing of the agreement on Monday in Riyadh, but we have reservations about some mediators involved in a conspiracy," he said.
Already angered by a Qatari call earlier this month for him to step down, Saleh accused Doha of having been an instigator of the unrest in Yemen.
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