* PM says guarantees include Turkish deputy
* Turkish commanders to be present at NATO command
(Recasts with quotes, details)
ANKARA, April 4 (Reuters) - Turkey said on Saturday it had dropped its objections to Dane Anders Fogh Rasmussen becoming the next head of NATO after U.S. President Barack Obama offered promises that one of Rasmussen's deputies would be a Turk.
Prime Minister Tayyip Erdogan, whose country had threatened to veto Rasmussen because of his handling of a 2006 crisis over cartoons of the Prophet Mohammad in a Danish newspaper, said Obama had also given Turkey guarantees that Turkish commanders would be present at the alliance's command.
"We explained our reservations on Rasmussen to Obama and he gave us guarantees on our reservations. Then our president accepted Rasmussen's candidacy," Erdogan told Turkish television.
"One of the issues is to have a Turk as one of his (Rasmussen) deputies and to have our commanders in NATO command," Erdogan told reporters in Ankara.
Turkey's objections to Rasmussen had threatened the image of unity NATO had sought to present at the military alliance's 60th anniversary summit.
It had also put the European Union-candidate at odds with France and Germany, which had strongly backed Rasmussen.
NATO is engaged in the biggest military operation in its history in Afghanistan, and Turkey, the only mainly Muslim member of the alliance, had said Rasmussen's appointment would exacerbate hostility towards the West in Muslim countries.
Rasmussen had defended the publication of the cartoons, which caused protests in the Muslim world, on the grounds of free speech and refused to apologise to Muslim countries.
But Turkey dropped its opposition at the last minute after Turkish President Abdullah Gul held private talks with Obama and Rasmussen, a Turkish official said.
"I acted responsibly as the prime minister of Turkey," Erdogan told Turkish television.
"One of the issues we put forward was how to improve relations by being more sensitive over the cartoon issue," Erdogan added. Rasmussen is scheduled to attend an international event on civilisations in Istanbul April 6-7.
Erdogan, who will host Obama on the same dates, said Turkey had brought up the issue with Obama of Kurdish ROJ TV, which has close links to the Kurdistan Workers' Party (PKK), a separatist guerrilla group, but is allowed to broadcast from Denmark.
Erdogan has said he has asked Rasmussen to shut down the station many times, but that the Dane had ignored his pleas.
The PKK, which has fought for an ethnic Kurish homeland in Turkey since 1984, is listed as a terrorist group in the United States and in the European Union. (Writing by Ibon Villelabeitia; Editing by Noah Barkin)
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