(Adds fresh attack, paragraphs 2, 3, more background)

By Daren Butler

SIRNAK, Turkey, June 9 (Reuters) - Thousands of people joined state-sponsored rallies in Turkey's mainly Kurdish southeast on Saturday to protest against increased attacks by separatist rebels of the banned Kurdistan Workers Party (PKK).

But hours after the rallies, which coincided with mounting speculation of a Turkish army incursion into nearby northern Iraq to hit PKK bases there, three soldiers were killed and six hurt by a landmine detonated by the rebels in Sirnak province.

The incident, which unusually claimed the lives of two officers as well as a private, will pile further pressure on Prime Minister Tayyip Erdogan's government to get tough with the rebels and perhaps send troops across the mountainous border.

Turkey's top generals have urged the government, which faces a strong nationalist challenge in national elections next month, to authorise an incursion into northern Iraq, where up to 4,000 PKK fighters are believed to be hiding.

Protesters at Saturday's rally, mainly state-paid village guards, civil servants and schoolchildren, waved Turkish flags and chanted anti-PKK slogans in the remote hillside town of Sirnak, overlooking the Iraqi border 50 km (30 miles) away.

"Damn the PKK", "Martyrs do not die, the homeland will not be divided", the crowds chanted below a 10 metre (33 ft) high portrait of modern Turkey's founder, Mustafa Kemal Ataturk, flanked by large Turkish flags hanging from a state building.

Diyarbakir, the largest city in Turkey's southeast, staged a similar anti-PKK demonstration on Saturday.

The rallies came a day after the General Staff in Ankara urged Turks to show a "mass resistance reflex" to PKK attacks.

More than 30,000 people have died in the conflict since the PKK took up arms in 1984 with the aim of carving out an ethnic homeland in the Kurdish southeast. Much recent rebel activity has focused on laying landmines targeting the armed forces.

PEOPLE DIVIDED

"I say damn the PKK. They killed our animals, they burned our houses, they kidnapped our children," said farm worker Mehmet Acet, 34, from a village which supplies militia forces who fight alongside the Turkish military.

Tens of thousands of Kurdish villagers across the southeast receive a monthly salary of around 500 lira ($373) as village guards, who in the past were often the targets of PKK attacks.

But the village guards acknowledged that many Kurds in the impoverished region remained sympathetic to the PKK's aims.

"In Sirnak, some are on one side and some on the other. Nearly all of us at this protest are village guards. We fight with the army against the PKK," said Kamil Bakir, 26.

He said he was forced to move to Sirnak from his village in 1990 after the militants killed members of his family.

Away from the tight security in the main square, local traders sat drinking tea and voiced sharply contrasting views on the demonstration.

"What they're holding is a rally against peace. Kurdish people just want peace ... The PKK offered a ceasefire and the state ignored this," said trader Hayri Gokce, 28.

The PKK has sometimes declared unilateral ceasefires, but Ankara calls them cosmetic and refuses to sit down and talk with a group it brands terrorist.

Underscoring regional tensions, Iraq's Foreign Ministry accused Turkey of "intensively shelling" northern Iraq this week and said it had handed Ankara's envoy a protest letter.

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