PARIS/BEIRUT- France is pressing Lebanese politicians to form a new government in a "reasonable timeframe" to lift the nation out of a deep crisis but has not fixed a new deadline after the last one in mid-September was missed, a French diplomatic source said.

Lebanon's Christian president, Michel Aoun, told fractious political leaders on Monday the country was heading "to hell" if a new cabinet was not formed swiftly to dig the nation out of its worst crisis since the 1975-1990 civil war.

But the nation's sectarian politicians remain deadlocked over how to pick ministers to draw up economic reforms.

Politicians had told President Emmanuel Macron during his visit after a huge August explosion in Beirut that they would form a cabinet of experts in 15 days, accelerating a process that usually takes months. That deadline passed last week.

Nerves in the nation were further rattled on Tuesday after a blast rocked southern Lebanon. A security source said it occurred at an arms depot of Hezbollah, a heavily armed and politically powerful Shi'ite Muslim group.

Political talks have hit a logjam over a demand by Hezbollah and its ally, Lebanon's other main Shi'ite group, the Amal Movement, that they name several ministers including the finance minister.

The source said Paris was reluctant to set a new deadline and was instead giving politicians more time provided they worked towards a French demand for a cabinet of ministers with expertise to deliver reforms.

"France is letting them move forward, but within a reasonable timeframe," the French source told Reuters.

France has said it was ready to host an international conference in the second half of October to secure aid from donors, who demand reforms before giving cash. Paris has drawn up a roadmap for a new government to tackle corruption and rebuild the economy.

But there has been no indication that Prime Minister-designate Mustapha Adib, a Sunni under Lebanon's sectarian system of power sharing, is any closer to naming a cabinet.

A senior Shi'ite political source said the two main Shi'ite groups insisted on choosing the finance minister or they would not take part in a government, a move that would likely mean any government policies would be blocked once sent to parliament. "Everyone is waiting," said another source familiar with the cabinet process. "I don't think the French initiative is dead."

(Reporting by Michel Rose in Paris and Tom Perry and Laila Bassam in Beirut; Writing by Michel Rose; Editing by Edmund Blair) ((michel.rose@thomsonreuters.com; +33149495071; Reuters Messaging: Twitter: https://twitter.com/MichelReuters))