(CNN) -- At least 35 Kurdish rebels have been killed in fighting in northern Iraq on Saturday, Turkey's military said Saturday as its offensive against the rebels came under criticism from Baghdad.
Turkish tanks on the move near the border town of Silopi in Sirnak province, southeastern Turkey.
The Associated Press quoted the military saying that the total number of rebels killed in its three day incursion was now 79, while two of its own soldiers died Saturday, bringing Turkey's death toll to seven.
The incursion against the Kurdistan Workers Party (PKK) in Iraq began late Thursday, marking a major escalation in Ankara's fight against the rebels.
Iraqi government spokesman Ali al-Dabbagh said Iraq's president and prime minister had urged Turkish officials to rethink the offensive, AP reported.
"We know the threats that Turkey is facing but military operations will not solve the PKK problem," al-Dabbagh said.
In a statement Friday, the Turkish military said it would act with "utmost sensitivity in order to avoid negative impact on local elements" -- a reference to keeping civilians out of the conflict.
"The Turkish Armed Forces, which values Iraq's territorial integrity and its stability, will return as soon as planned goals are achieved," the military 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."
Turkey has been taking cross-border military action, including airstrikes and artillery shelling, against the PKK in retaliation to attacks by the group on targets in Turkey from bases in the Kurdish region of northern Iraq.
Turkey has also been carrying out small ground operations into Iraq, forays characterized as "hot pursuit" incursions with a few hundred commandos responding to a particular threat.
Citing Turkish media reports estimating that as many as 10,000 Turkish troops had been involved, Fadi Hakura, an analyst with UK military thinktank Chatham House, said the operation was the first major incursion by Turkey into Iraq since Hussein was toppled in 2003.
Hakura said the Turkish military wanted to conduct a surprise attack against the PKK prior to the springtime, when violent attacks tend to escalate, and when the snow in the mountainous border region leaves the fighters' footprints.
"Normally during the 1980s and the 1990s, the incursions involved 35,000 50,000 troops and they tended to be somewhat open-ended over weeks. This one is expected to be limited to a matter of days and targeted attacks against the PKK," he said.
U.S. officials were downplaying the scope of the operation Friday.
Tom Casey, deputy State Department spokesman, said Iraqi Foreign Ministry Hoshyar Zebari called the incursion "limited in nature" and not "major."
"The PKK is a common enemy of the U.S., Turkey and Iraq. We need to work together to resolve it," Casey said. "We are pleased that Turks have stressed that they will do everything possible to avoid acts that would harm civilians."
Rear Adm. Gregory Smith, a spokesman for the U.S. military in Iraq, told CNN the military is "aware" of a Turkish "operation of limited duration to specifically target PKK terrorists in that region."
"Turkey has given its assurances it will do everything possible to avoid collateral damage to innocent civilians or Kurdish infrastructure," Smith said.
The ground troops' deployment followed cross-border shelling early Thursday by Turkish soldiers into abandoned villages north of Irbil -- the capital of Iraq's Kurdish Regional Government.
The shelling, which struck abandoned villages in the Khwar-Kork area north of Irbil, lasted two hours and was followed by heavy gunfire, a KRG official told CNN. There were no reports of casualties.
Border tensions have been a source of diplomatic disagreement between the U,S. and its Iraqi and Turkish allies. U.S. and Iraqi authorities have been concerned that any large-scale operation by Turkey into Iraq to chase down Kurdish rebels could destabilize the region.
At the same time, the U.S. backs Turkey's efforts to battle the PKK, which both countries regard as a terrorist group and has been providing intelligence to the Turks.
"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," Smith said. E-mail to a friend