By Tarek Amara

TUNIS (Reuters) - Tunisia on Saturday launched a crackdown on mosques and radio stations associated with hardline Islamists after militants killed 14 soldiers in an area near the country's border with Algeria.

The move underscores the difficulty one of the Arab world's most secular countries faces in dealing with the rise of conservative Islamist movements and militants since the 2011 revolt that ousted autocrat Zine El-Abidine Ben Ali and opened the way to democracy.

Tunisia's armed forces have been carrying out a campaign to flush out militants from their remote hideout in the Chaambi mountains on the border with Algeria. Some of the militants are tied to al Qaeda and 14 soldiers were killed this week when dozens of gunmen with rocket-propelled grenades attacked two army checkpoints in the region.

"The prime minister has decided to close immediately all the mosques that are not under the control of the authorities, and those mosques where there were reported celebrations over the deaths of the soldiers," the office of Prime Minister Mehdi Jomaa said in a statement.

It said the government would also order the closure of radio stations, websites or television stations that publish messages from militant groups. More than 60 Islamists linked to militants had also been arrested since the attacks on the army checkpoints, the statement said.

It did not give any figures for mosques included in the crackdown or name any websites or media.

Tunisia is one of the main sources of Islamist militants traveling from North Africa to fight with radical groups in Iraq and Syria. The government is concerned hardliners have been spreading their jihadist message at mosques not controlled by the state.

The government has been slowly taking back control of mosques taken over by ultra-conservative Salafist groups since the 2011 uprising.

Tunisia has been praised as a model of transition to democracy in the aftermath of the uprising. The country has adopted a new constitution, and a transition government has taken over until elections this year to overcome a crisis between a leading Islamist party and its secular rivals.

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But militants from one hardline group were blamed for killing two secular opposition leaders last year and triggering a political crisis that eventually forced the governing moderate Islamist party to make way for a caretaker administration.

Al Qaeda in the Islamic Maghreb, the group's north Africa branch, has claimed attacks in Tunisia in the past, but another militant group, Ansar al Sharia, listed as a terrorist organization by Washington, is also active.

(Writing by Patrick Markey; Editing by Tom Brown)