It is the second air attack on the PKK in as many days.
On Sunday, Turkish fighter jets bombed Kurdish rebel targets inside Iraqi territory, in the fourth cross-border operation against the Kurdistan Workers’ Party, or PKK, in one week.
Barzani refused to meet Condoleezza Rice, the US secretary of state, when she made a surprise visit to Iraq on December 18.
However, George Bush, the US president, took the opportunity on Monday to promise Turkey his country would continue to help fight separatist Kurdish rebels.
Recep Tayyip Erdogan, the Turkish prime minister, agreed with Bush to continue to share intelligence. Turkey maintains it has the right to pursue PKK fighters into Iraqi territory.
Gordon Johndroe, a spokesman for the National Security Council at the White House, said the leaders discussed the “importance of the United States, Turkey and Iraq working together to confront” the rebels.
Both Washington and Baghdad have asked Turkey to show restraint, fearing a large-scale Turkish offensive might destabilise northern Iraq.
Jalal Talabani, the Iraqi president who is a Kurd, said Iraq‘s foreign minister had summoned the Turkish ambassador in Baghdad to complain, but said he did not want to exacerbate tensions between Iraq and its neighbour.
Talabani also told the reporters that the two main Kurdish parties, the Democratic Kurdistan party and Patriotic Union of Kurdistan, have agreed with the Iraqi Islamic party, to set up what he described as a long-term relation.
Talabani said the new alliance was aimed “at finding a political ground in Iraq that combines all parties and be a prelude to the establishment of a real national unity government”.
Tariq Hashemi, Iraq’s vice-president, said that the agreement was not against any party, but part of political changes facing politicians in Iraq.