About 10,000 Turkish troops are taking part in an offensive against Kurdish rebels in southeastern Turkey and northern Iraq, a day after rebel raids near the border killed 24 Turkish soldiers and wounded 18 others.

In a statement posted on its website Thursday, Turkey's military command said a large-scale land operation backed by airstrikes has begun in five separate areas of Turkey and northern Iraq. It did not specify the exact locations. The report says some 22 battalions are involved, with helicopter gunships backing them up. It is Turkey's largest offensive against the rebels since February of 2008. It is unclear how many of the soldiers are inside Iraq.

In a statement Thursday, the Iraqi government condemned the rebel attacks and promised to work with Ankara to prevent such attacks in the future.

The outlawed Kurdistan Workers' Party, or PKK, on Wednesday claimed responsibility for the attacks, which were some of the rebels' deadliest against the Turkish military since their nearly three-decade-old insurgency began.

The attacks have outraged many Turks, with thousands, many of them students, marching through the capital, Ankara, on Thursday in a show of support for the military. Many chanted slogans denouncing terrorism.

The PKK has stepped up attacks against Turkish targets in recent weeks. Turkish forces have responded by increasing the number of airstrikes against suspected rebel bases in northern Iraq. Turkey called on Iraq last week to stop the Kurdish rebels from attacking Turkey from Iraqi soil, saying its “patience is running out.”

Kurdish rebels have waged a campaign for autonomy in Turkey's largely Kurdish southeast since 1984. The fighting has killed more than 40,000 people. Turkey, the United States, and the European Union regard the PKK as a terrorist group.

The Turkish government has taken steps to address the demands of Kurds and other minorities for greater rights. Prime Minister Erdogan is pushing to amend the constitution, which was written in 1982 when Turkey was under military rule. But Kurdish leaders say an amended constitution should recognize the Kurds as a distinct element of the nation and grant them autonomy.