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French Foreign Minister Jean-Marc Ayrault attends a meeting with a group of International CEO's during a Strategic Attractiveness Council at the Elysee Palace, in Paris, March 22, 2016. REUTERS/Gonzalo Fuentes

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PARIS (Reuters) - France hopes to reopen its embassy in Tripoli as a sign of support for Libya's new unity government, Foreign Minister Jean-Marc Ayrault said on Tuesday, in what would be the first reopening of a Western diplomatic mission there.

Western governments are growing increasingly concerned about Islamic State's success in establishing a firm foothold in Libya while two rival factions operating two governments fought for power.

The West is now backing a U.N.-brokered national unity government, which arrived in Tripoli from Tunisia last week and has been operating from a naval base as it seeks to establish its authority.

"Tunisia has reopened its embassy ... We are working on it if the security conditions are guaranteed ... It would be an extremely strong signal to show that we don't give in to terrorists," Ayrault told reporters after a meeting with his German counterpart, Frank-Walter Steinmeier.

Ayrault, who described the arrival of the government as an important milestone, said Paris hoped to open its embassy "as soon as possible".

Western diplomatic staff were evacuated from Tripoli in 2014 amid heavy fighting between rival factions.

European Union sanctions, pushed by Paris, went into effect last week to pressure hardliners to accept the U.N. efforts to unite factions and militias that have competed for power since the fall of Muammar Gaddafi in 2011.

Paris took a leading role in the NATO air campaign that helped rebels overthrow Gaddafi, and French aircraft are now conducting reconnaissance flights over Libya while French military advisers operate on the ground in conjunction with Britain and the United States.

Asked what further military aid Paris could provide, Ayrault said: "If the Libyan government asks us for help to ensure its security, we are available, but ... there is no question of us deciding anything in their place, especially after what happened in 2011."

(Reporting by John Irish; Editing by Kevin Liffey)

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