The Iraqi president, Jalal Talabani, today told Turkey not to "violate" the country after Turkish troops entered northern Iraq to attack Kurdish rebels.

Several hundred troops – some reports claimed thousands - crossed the border after fighter jets and heavy artillery bombed Kurdistan Workers' party (PKK) forces.

The PKK said two Turkish soldiers were killed and eight wounded in clashes following the incursion, but Turkey refused to comment on the claim.

A rebel spokesman pledged that fighters would "prevent Turkish army from entering deep in the Iraqi land".

The Turkish prime minister, Recep Tayyip Erdogan - who said he had given both his Iraqi counterpart, Nouri al-Maliki, and the US president, George, Bush advance warning - defended the raid as "just". He said the only targets were "PKK camps located in the north of Iraq".

However, a Baghdad spokesman said Talabani had told the Turkish head of state, Abdullah Gul, that Ankara "should respect Iraq's unity and sovereignty and not violate its lands".

The spokesman added that Iraq considered the PKK's actions in Turkey to be "terrorist".

In a statement, Turkish military officials said the incursion had been launched yesterday evening.

"The Turkish armed forces, which value Iraq's territorial integrity and its stability, will return as soon as planned goals are achieved," the statement said.

"The executed operation will prevent the region from being a permanent and safe base for the terrorists, and will contribute to Iraq's stability and internal peace."

NTV television reported that 10,000 troops were taking part in the offensive and had penetrated 10km (six miles) into Iraq, although one US officer said the offensive involved only several hundred troops.

Rear Admiral Gregory Smith, a spokesman for US forces in Iraq, said Turkey had assured the US it would do everything possible to avoid "collateral damage" to innocent civilians and infrastructure.

"The United States continues to support Turkey's right to defend itself from the terrorist activities of the PKK and has encouraged Turkey to use all available means, to include diplomacy and close coordination with the government of Iraq to ultimately resolve this issue," he added.

Reuters reported that the deputy assistant secretary of state, Matthew Bryza, said the offensive was "not the greatest news" and took Turkey's confrontation with Iraq-based Kurdish fighters to a "whole new level".

A spokeswoman for the European commission appealed to Turkey to act with restraint, saying: "Turkey should refrain from taking any disproportionate military action and respect human rights and the rule of law."

The offensive is the latest Turkish operation against the PKK, which it accuses of using Kurdish northern Iraq as a base to launch attacks on south-east Turkey in its long-running campaign for autonomy in the region.

The US, the EU and Turkey consider the PKK to be a terrorist organisation.

In December, several hundred Turkish troops carried out a smaller ground incursion, and Ankara has also launched air and artillery strikes against suspected PKK targets in Iraq.

Its parliament authorised the army to carry out such raids in October.

Fouad Hussein, a spokesman for the semi-autonomous Kurdish government, said Kurdish Peshmerga forces had been put on alert.

He added that Iraqi Kurdish forces also had tightened security around bases housing Turkish military monitors operating in northern Iraq with permission from local authorities under a 1996 agreement.

"The government of Kurdistan ordered the Peshmerga forces to be on alert in fear of any Turkish incursion on Iraqi territory," he said, claiming Turkish military monitors had tried to leave their bases in violation of the 1996 agreement.

Turkey has staged ground incursions against Turkish Kurd rebels in northern Iraq in previous years.

The PKK launched its guerrilla campaign in 1984, and as many as 40,000 people have died.