By Tulay Karadeniz

ANKARA (Reuters) - Turkish President Tayyip Erdogan said on Tuesday it was impossible to continue a peace process with Kurdish militants and urged parliament to strip politicians with links to them of immunity from prosecution.

Hours after he spoke, the Turkish military said its F-16 fighter jets had bombed Kurdistan Workers Party (PKK) militants in the southeastern Turkish province of Sirnak, which borders Iraq, in response to an attack on a group of gendarmes.

Turkey last week launched air strikes on PKK camps in northern Iraq following a series of attacks on its police officers and soldiers blamed on the Kurdish militant group.

The PKK has said the air strikes, launched virtually in parallel with strikes against Islamic State fighters in Syria, rendered the peace process meaningless but stopped short of formally pulling out.

"It is not possible for us to continue the peace process with those who threaten our national unity and brotherhood," Erdogan told a news conference in Ankara before departing on an official visit to China.

Western allies have said they recognize Turkey's right to self-defense but have urged the NATO member not to allow peace efforts with the PKK to collapse. While deeming the PKK a terrorist organization, Washington depends heavily on allied Syrian Kurdish fighters in battling Islamic State in Syria.

An emergency NATO meeting in Brussels on Tuesday offered political support for Turkey's campaigns in Syria and Iraq, and Erdogan signaled Turkey may have a "duty" to become more involved.

For NATO allies, the prospect of Turkey, which borders Iran, Iraq and Syria, fighting a domestic conflict against Kurdish as well as Islamist fighters is a deep concern. But for many in Turkey, Kurdish rebellion remains the primary national threat.

Besir Atalay, spokesman for the ruling AK Party, said it was too soon to declare the peace process over and said it could resume if "terrorist elements" put down arms and left Turkey.

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"There is currently a stagnation in the mechanism but it would restart where it left off if these intentions emerge," he told a press conference in Ankara.

POLITICAL GAMBLE

Braving nationalist anger, Erdogan introduced tentative reforms on Kurdish rights and in 2012 launched negotiations to try to end a PKK insurgency that has killed 40,000 people since 1984. A fragile ceasefire had been holding since March 2013.

However, any calculation Erdogan may have had that his political gamble would reap broad electoral support from Kurds, some 20 percent of the population, demonstrably failed.

The pro-Kurdish HDP party won 13 percent of the vote in a June 7 poll, helping to deprive the AKP Erdogan founded of a majority in parliament for the first time since 2002.

Many Kurds believe that by reviving conflict with the PKK, Erdogan seeks to undermine support for the HDP ahead of a possible early election. That poll - so runs the argument - could then provide him with the majority he seeks to change the constitution and increase his powers.

"He is trying to achieve the result he failed to in the June 7 election in a political coup. That's the real aim of the steps taken now," the PKK said in an e-mailed statement.

It accused Erdogan of trying to "crush" the Kurdish political movement "to create an authoritarian, hegemonic system", but it did not directly address his latest comments.

Turkey has shut down almost all Kurdish political parties over the years. Erdogan, who has accused the HDP of links to the PKK, said he opposed party closures but urged parliament to lift the immunity of politicians with links to "terrorist groups".

"We have committed no unforgivable crimes. Our only crime was winning 13 percent of vote," HDP chairman Selahattin Demirtas told party members in parliament.

"The only way for the AKP to be in government on its own is if the HDP is liquidated. Tomorrow the HDP's 80 lawmakers will submit a request for immunity to be lifted," he said, effectively challenging parliament to fulfill Erdogan's threat.

SEEKING LEGITIMACY

Casting the operations as a war on terrorist groups "without distinction", Turkey opened its air bases to the U.S.-led coalition against Islamic State and launched air strikes against the jihadists in Syria and the PKK in northern Iraq last week. It has since been rallying international support.

"No steps back will be taken in our fight against terrorism. This is a process and it will continue with the same determination," Erdogan said, after phone calls overnight with French President Francois Hollande, the king of Saudi Arabia and the emir of Qatar.

Presidential sources said all three leaders had expressed their support.

But Western allies are also concerned that Erdogan should not abandon several years of work on a peace process with the PKK, which has entailed giving Kurds more cultural rights with the prospect, over time, of greater autonomy in the southeastern regions where they constitute a majority.

"Dangerous rhetorics in Turkey against HDP, which won 6 million votes in last elections. Time to face that reality," the European parliament's Turkey rapporteur Kati Piri wrote on Twitter.

Turkish officials reject the notion that the action against the PKK is motivated by domestic politics, pointing to a series of militant attacks on the security forces in recent weeks.

On Monday, a gendarmerie major in the eastern province of Mus died after being shot by suspected PKK militants, while in the nearby province of Van a military unit came under fire.

There have been more attacks since the air strikes began. Suspected PKK militants blew up a bridge late on Monday on a major highway in the southeast, while gunmen attacked a soldier in the town of Semdinli, triggering clashes. The military said the soldier later died, at least the fourth member of the security forces to be killed over the past week.

(Additional reporting by Humeyra Pamuk and Ayla Jean Yackley in Istanbul; Writing by Nick Tattersall; Editing by Giles Elgood)