(Reuters) -

Tunisian police shot dead an Islamist militant in Tunis and a soldier was killed in a blast near the Algerian border on Sunday, as the government grappled with growing security and political crises in the country.

There has been a surge in Islamist militant attacks over the past two weeks in the North African country, and on Friday security forces launched heavy air and artillery strikes on militant hideouts in the Mount Chaambi area near the Algerian border.

At the same time the secular opposition, angered by the assassination of two of its leading members and emboldened by Egypt's army-backed ousting of its elected Islamist president, is seeking to topple its own moderate Islamist-led government.

Tens of thousands of Tunisians came out in a show of force for the ruling Ennahda party on Saturday. The opposition has pledged to rally even more supporters in its own demonstration later on Sunday.

One soldier was killed and seven others were wounded in a landmine that hit their tank as they combed an area in Mount Chaambi where militants killed 8 soldiers earlier this week, in the deadliest attack on Tunisian forces in decades.

In the capital Tunis, interior ministry official Lotfi Hidouri police raided a house where militants were hiding weapons in the Kabaria district. "The police killed a terrorist and arrested five others," he said.

Witnesses said police also arrested several hardline Salafists suspected of ties to militant groups in the town of Sbitla, north of the capital.

One witness said dozens of Salafists then gathered at the police headquarters in Sbitla to protest against the arrests and that the police fired in the air to disperse them.

Over the past week, a roadside explosive device and a car bomb have targeted security forces in Tunis, the first such attacks to hit the capital. No one was hurt.

ARAB SPRING MODEL

Once considered a model among fledgling "Arab Spring" democracies, Tunisia is facing its worst crisis since protesters toppled autocrat Zine el-Abidine Ben Ali and set off a wave of uprisings across the region.

The opposition has accused Ennahda of being linked to or tolerating Islamist militant attacks. The party denies that and has stepped up recent efforts to crack down. It denounced recent attacks as terrorism.

Demonstrations swept Tunisia after the assassination of a Mohamed Brahmi, a member of the Arab nationalist Popular Front party, on July 25. The killing followed the assassination of party leader Chokri Belaid in February.

Prime Minister Ali Larayedh told journalists on Sunday a man suspected of ties to the Belaid assassination was captured by security forces. He called on militants to turn themselves in.

"I call on the terrorists being hunted by security forces to turn themselves in. There is no future in terrorism," he said, speaking outside the interior ministry, where he had been meeting officials.

The ministry is due to give a news conference on Sunday evening.

The air and artillery strikes by security forces in the Mount Chaambi area were launched after the deadly attack on soldiers earlier in the week.

State Tataouin radio and other local media reported on Sunday that Tunisian forces had killed 10 militants in Chaambi and arrested three others.

No security officials were willing to comment.

A day earlier, on Saturday, tens of thousands of Tunisians crowded into the Kasbah Square in a show of force for the Ennahda-led government.

"No to coups, yes to elections!", they shouted, in one of the biggest demonstrations since the 2011 revolt.

This Sunday night, the opposition aims to bring out even bigger crowds to rally against the government. It is also planning a mass protest on Wednesday to mark the six-month anniversary of Belaid's assassination.

(Writing by Erika Solomon; Editing by Pravin Char and Sonya Hepinstall)

By Tarek Amara