* Bomber sought to target hotel in Tunisian resort
* Government is cracking down on hardline Islamists
* Libya chaos exploited by Tunisia's militants
By Tarek Amara
TUNIS, Oct 30 (Reuters) - A suicide bomber blew himself up in the Tunisian tourist resort of Sousse on Wednesday, the first such assault since 2002 in a country now battling Islamist militants empowered by chaos in neighbouring Libya.
Police foiled another attack when they arrested a would-be suicide bomber at former President Habib Bourguiba's tomb in the seaside town of Monastir, security sources said.
No group has claimed responsibility for the attacks, but the Islamist-led government has been combating Ansar al-Sharia militants it says are tied to al Qaeda's North Africa affiliate.
The first bomber had initially sought to enter a hotel in Sousse with a suitcase, police said. "The bomber had tried to get into the hotel, but when he was not allowed in, he ran onto the beach and blew himself up," a security source said.
The bombing is bad news for the vital tourism industry in Tunisia, which attracted 5.8 million mostly European visitors to its Mediterranean beaches and desert tours in 2012. Tourism is still recovering from the 2011 uprising that toppled the North African country's autocratic leader Zine al-Abidine Ben Ali.
Since then, Islamists have pressed for strict Sharia law to be imposed in one of the Muslim world's most secular countries.
The rise to power of an elected Islamist-led government has fuelled fears of many secular Tunisians that women's rights and liberal educational traditions may be eroded.
The ruling Ennahda party says even ultra-orthodox Islamist views must be accommodated in Tunisia's fledgling democracy, but that there is no place for armed Islamist militants.
The authorities say such militants have acquired weapons and training in neighbouring Libya, where the central government has failed to impose order since Muammar Gaddafi fell in 2011.
Ennahda accused Ansar al-Sharia militants of being behind the assassination of two secular opposition leaders this year.
Those attacks set off months of protests from opposition supporters who said Ennahda had been too lenient on hardline Islamists. Ennahda has agreed to step down within the next three weeks to end the unrest and allow a caretaker government to govern until elections.
Ansar al-Sharia was also blamed for inciting the attack on the U.S. embassy a year ago, when Islamist protesters stormed the building. The group's leader is a former al Qaeda veteran who once fought in Afghanistan.
Nine Tunisian policemen were killed in clashes with militants earlier this month in two different cities.
Al Qaeda in the Islamic Maghreb operates in North Africa alongside groups such as Ansar al-Sharia and fighters loyal to Mokhtar Belmokhtar, blamed for the attack on Algeria's Amenas gas plant in January where nearly 40 foreign workers died.
Al Qaeda carried out Tunisia's only previous suicide bombing in 2002 when 21 people were killed at a synagogue on the island of Djerba.
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