Pro-Kurdish demonstrators angered by Turkey's lack of action in the fight against jihadists on the Syrian border clashed with police across the country Tuesday, leading to at least three deaths and several people wounded.

One young pro-Kurdish protester was killed in the southeastern city of Mus while police used tear gas and water cannon to disperse angry protests in Istanbul.

There were conflicting reports about how the 25-year-old protester was killed in the clashes in Mus, with the Hurriyet newspaper saying he died of a gunshot wound after being caught in crossfire.

But NTV television said he was killed after being struck in the head by a tear gas cannister fired by police to disperse the protesters.

In Diyarbakir, Turkey's largest Kurdish city in the southeast, two people were killed and 10 others were injured after Islamist groups opened fire on demonstrators.

Turkey's Justice and Development Party (AKP) government has so far not intervened militarily against Islamic State (IS) jihadists fighting for the Kurdish border town of Kobane, to the fury of Turkey's Kurds.

Turkey's main pro-Kurdish party, the People's Democratic Party (HDP), late Monday called for street protests "against IS attacks and the AKP's stance on Kobane".

Prime Minister Ahmet Davutoglu has vowed that Turkey will do whatever necessary to prevent the fall of Kobane.

But Kurds bitterly accuse Ankara of merely looking on as the town risks being overrun by jihadists despite the dozens of Turkish tanks deployed on the border.

Almost all shops were closed in Mus, where where dozens of youths set fire to bins and lit smoke bombs and firecrackers. Another person was seriously injured.

In Istanbul's Gazi neighbourhood, largely populated by Kurds, police used tear gas and water cannon to disperse a protest by several hundred Kurds, an AFP correspondent reported.

Elsewhere in Istanbul, one person was seriously injured after being shot in the head from close range.

In Diyarbakir, enraged youths overnight torched a police vehicle, scores of vehicles and shops and attacked government offices.

Clashes also took place in the Turkish capital Ankara, with several police injured in the protests.

Violent protests were also reported in other cities including Mersin and Adana in the south. A curfew was declared in the Kurdish-majority provinces of Mardin, Siirt and Van.

Kurds have been particularly irked by the reluctance of the Turkish authorities, who are themselves worried by Kurdish separatism, to allow Kurdish fighters over the border into Syria.

They have warned that the fall of Kobane could mean an end to the peace talks between Ankara and the PKK, which waged a deadly insurgency in Turkey for the last three decades but has largely observed a ceasefire since last year.

Jailed PKK leader Abdullah Ocalan said in a message relayed by his brother that the government had until mid-October to show it was serious about the peace process.

"They (the government) are talking about resolution and negotiation but there is no such thing," he said.

"This is an artificial situation, we will not be able to continue anymore," said the statement carried by the Firat news agency.

"The state must take action... Can a peace process make any progress this way?"

Kurdistan Communities Union (KCK) -- considered the urban wing of the mountain-based PKK -- called on "millions" to take to the street to protest against "IS brutality".