Turkey's military said the cross-border offensive, possibly the largest in a decade, would continue until they had stopped the threat from PKK rebels, who have been using northern Iraq as a base to stage attacks in Turkey.
It said in a military statement 24 Kurdistan Workers Party (PKK) rebels and five soldiers were killed in clashes in Iraq. It also said at least 20 rebels were killed in separate aerial attacks.
The United States urged Turkey, a key regional ally, to limit its offensive to precise PKK targets and to bring the operation to a swift conclusion. Iraq's government called on Turkey to respect its sovereignty and to avoid any military action which would threaten security.
The European Union and the United Nations also urged restraint, fearing the offensive could jeopardise the most stable region in Iraq at a time when security is improving, and also rekindle tensions between Turks and ethnic Kurds.
The Turkish military said its troops had entered Iraq late on Thursday to destroy PKK camps and hunt rebels, which has been battling for decades to create a Kurdish homeland in southeast Turkey.
"The operations inside Iraq will intensify tomorrow," said a Turkish military source, who declined to be named.
Turkish television said between 3,000 and 10,000 soldiers had entered Iraq, but several Iraqi officials and a military source with US-led coalition forces in Baghdad said only a few hundred troops were involved.
The senior Turkish military source said two brigades made up of around 8,000 troops had taken part in the offensive.
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