February 23, 2008 | By ALISSA J. RUBIN and SABRINA TAVERNISE

BAGHDAD — Turkey’s military said Friday that it had sent troops into northern Iraq on Thursday night, in what Prime Minister Recep Tayyip Erdogan of Turkey called a limited operation to weaken Kurdish militants there.

At least 24 Kurdish fighters and 5 Turkish soldiers were killed during the ground operation on Friday, the Turkish military said, with at least 20 more fighters believed to have been killed in later artillery and air attacks. The operation, which continued into the night, destroyed a number of hide-outs and military caches, the military said.

Earlier on Friday, Mr. Erdogan described the mission as “limited” in size and emphasized that the soldiers would return to Turkey “in the shortest possible time.”

The operation on Friday appeared to have been the largest ground incursion by Turkey into Iraq since the American invasion in 2003, but was not a sweeping offensive on the scale that the United States had once feared.

Iraq’s foreign minister, Hoshyar Zebari, called the operation an “escalation” and said the Iraqi government had protested to Turkey and asked it “to withdraw Turkish troops from Iraqi territory.” Mr. Zebari said five bridges were destroyed in the operation, despite Turkey’s assurances that no civilian infrastructure would be touched.

Reports of the numbers of troops varied. Mr. Zebari said he believed that only a few hundred soldiers had crossed the border, while Turkish television reported that the number was about 10,000. According to Reuters, several Iraqi officials and a source with American-led forces in Iraq said only a few hundred troops were involved.

“The target, purpose, size and parameters of this operation are limited,” Mr. Erdogan said in televised comments from Ankara, Turkey’s capital. Mr. Zebari, in an interview in Baghdad, said: “The troops are special forces or foot soldiers being ferried in by helicopter. Also, these are areas that have a lot of snow, and that limits the movement of troops.”

In Baghdad, Rear Adm. Greg Smith, referring to the militants’ group, the Kurdistan Workers’ Party, or P.K.K., described the attack as “an operation of limited duration to specifically target P.K.K. terrorists in that region.”

The militants want greater autonomy for Turkey’s Kurdish minority and have fought the Turkish military from hide-outs in Turkey and Iraq for decades.

In Erbil, the northern Iraqi region’s capital, Kurdish leaders huddled in meetings with Kurdish military leaders and issued only brief statements to the news media.

However, the tone of statements both from the Kurds and the Americans suggested that they were trying to tamp down nationalist sentiments and avoid inflammatory language.

The president of the semiautonomous Kurdistan Regional Government, Massoud Barzani, who often takes a bellicose tone, especially when talking about Turkey, was measured in his response and steered clear of threatening retribution. “We prefer that this would be solved politically,” he said.

“This trespasses on the Kurdistan region’s sovereignty and on Iraq’s sovereignty,” Mr. Barzani said. “We are not working to complicate the situation, but we will defend ourselves.”

Mr. Erdogan said that he had called President Bush around midnight to tell him of the operation and that he had called Prime Minister Nuri Kamal al-Maliki of Iraq. The White House said Turkey had informed the United States beforehand.

“Turkey has given its assurances it will do everything possible to avoid collateral damage to innocent civilians or Kurdish infrastructure,” Admiral Smith said.

Admiral Smith added that the United States backed Turkey’s right to rout the terrorists who have used mountain camps across the border of Iraqi Kurdistan to stage attacks on Turkey.

The conflict has been difficult for the United States because it sets Turkey, a NATO member and one of its closest allies in a troubled region, against the Iraqi Kurds, important American partners in the war in Iraq.

The Bush administration agreed to share information and to open airspace to the Turkish military last year, after attacks by the Kurdish group intensified. Turkey’s airstrikes against Kurdish targets, which began in December, were sanctioned by the United States.

Some American officials struck troubled tones. A deputy assistant secretary of state, Matthew J. Bryza, said the incursion was “not the greatest news,” Reuters reported from Brussels. In a report from Washington, Reuters said a Pentagon spokesman said the United States military had urged Turkey to bring the operation to a “swift conclusion.”

Even so, a flurry of recent visits by senior military commanders of both countries, including one this month in Washington by Gen. Ergin Saygun, Turkey’s deputy military chief, seem to indicate a relatively high level of cooperation.

The operation is “more than a random hunt,” said Sedat Laciner, director of the International Strategic Research Organization, based in Ankara. It is “based on advanced technology, international cooperation and fine targeting.”

The Turkish military said the reason for the operation was to “prevent the region from being a permanent and safe base for the terrorists.”

The European Union’s foreign policy chief, Javier Solana, speaking in Slovenia, said, “We think this action is not the best response,” Reuters reported. “The territorial integrity of Iraq is for us very important.”

Turkish domestic politics were also in play. The military’s image was damaged in bruising political battles with Mr. Erdogan and his party last year, and a successful campaign against a common enemy could help repair it.

“Their success would ultimately help their image to get stronger,” Mr. Laciner said.

On Friday afternoon, the military air base in the southeastern Turkey town of Diyarbakir was buzzing with activity, said the state-run Anatolian News Agency, which reported that fighter jets and helicopters were taking off to monitor the border.

Alissa J. Rubin reported from Baghdad, and Sabrina Tavernise from Samsun, Turkey. Sebnem Arsu contributed reporting from Istanbul, Balen Younis from Baghdad, and an Iraqi employee of The New York Times from Iraqi Kurdistan.