President Abedrabbo Mansour Hadi, who has been based in Yemen's second city Aden since escaping the Shiite militia-controlled capital last month, made the request after failing to reach agreement with the militia and their backers on a venue inside Yemen.
UN-brokered reconciliations talks, which had been taking place in Sanaa, have broken down since Hadi's flight to Aden.
The Western-backed president insists they can no longer be held in the capital and the militia and their supporters have threatened to boycott talks anywhere else.
"The secretariat general of the Gulf Cooperation Council is going to make the necessary arrangements" for the talks which Hadi requested in a message to Saudi Arabia's King Salman, the royal cabinet said.
It did not give a date for the talks.
Hadi proposed that the Riyadh meeting convene "all the Yemeni political parties anxious to preserve the security and stability of Yemen," said the statement carried by the official SPA news agency late on Sunday.
He underlined that the conference should reject "the coup d'etat" of the Huthi militia, who seized power in Sanaa on February 6 after overrunning the capital last September.
Several GCC states, led by Saudi Arabia, have moved their embassies to Aden after an exodus of foreign diplomats from Sanaa in February over security concerns.
The Cairo-based Arab League meanwhile welcomed the Riyadh talks and expressed "solidarity" with Yemen's Foreign Minister Abdullah al-Saidi who remains under house arrest.
Signup to our newsletter and follow us on Facebook and Twitter!
"The Arab League demands that his house arrest be lifted so he can perform his patriotic and nationalist mission under the legitimate authority of President Abedrabbo Mansour Hadi," said a statement issued by the League late on Monday after a meeting of its foreign ministers.
The six Sunni-ruled Gulf states are deeply suspicious of the Huthis, fearing they will take Yemen into the orbit of Shiite Iran.
Yemen, on the frontline in the US war against Al-Qaeda, has been gripped by unrest since longtime president Ali Abdullah Saleh stepped down in early 2012 after a bloody year-long uprising.
Saleh's General People's Congress party is widely accused of backing the Huthis and has vowed to boycott any talks not held in Sanaa.
The Huthis control much of northern Yemen but have faced fierce resistance from armed tribes in mainly Sunni and confessionally mixed provinces south of the capital, sometimes in alliance with Al-Qaeda.
Tribal sources said 22 militiamen were killed in fighting in Al-Baida province Sunday night but the toll could not be independently verified.
Troops and paramilitaries loyal to Hadi largely control Aden and adjacent southern provinces but Al-Qaeda has a strong presence further east.
An attack by suspected Al-Qaeda militants on an army position on the border between Abyan and Shabwa provinces killed four soldiers on Monday, a military official told AFP.
The militants lost seven of their men before retreating to the east, a tribal source said.