BEIRUT  - Lebanon's prime minister-designate on Monday called for cooperation from all sides in the formation of a new government and for efforts to secure the immediate success of a French initiative to lift the country from crisis.

Lebanon is in the throes of an economic crisis marking the worst threat to its stability since the 1975-90 civil war. But French efforts to get its fractious leaders to agree a new government to start fixing the problems have yet to bear fruit.

The cabinet formation process has hit a logjam over the demand of Lebanon's two dominant Shi'ite parties, the Iran-backed Hezbollah and its ally the Amal Movement, to name Shi'ite ministers in cabinet including the finance minister.

All sides should cooperate for the formation of a government of specialists "capable of halting the collapse and starting work to get the country out the crises", Prime Minister-designate Mustapha Adib said in a statement.

Adib said he would spare no effort "to achieve this goal in cooperation with the president".

Last week, reports suggested Adib may resign as his efforts floundered. He had proposed switching control of ministries, some of which have been held by the same factions for years.

A senior Lebanese political source said France was still working to try to find a way through the logjam.

Adib is a Sunni Muslim as required by a power-sharing system that parcels out posts according to religious sects. He is backed by former Lebanese prime ministers including Saad al-Hariri, Lebanon's leading Sunni.

The standoff spilled into the religious domain on Sunday.

Lebanon's senior Christian cleric, Maronite Patriarch Bechara Boutros Al-Rai, criticised the demands made by the main Shi'ite parties without naming them, asking how one sect could demand "a certain ministry".

This prompted a response from the supreme religious body of Lebanon's Shi'ites which said comments by a major religious leader had distorted the truth.

(Writing by Tom Perry; Editing by Alex Richardson and Raissa Kasolowsky, William Maclean) ((thomas.perry@thomsonreuters.com; Reuters Messaging: thomas.perry.reuters.com@reuters.net))