(Adds quotes from Erdogan statement, background)

WASHINGTON, Feb 16 (Reuters) - U.S. President Barack Obama has told Turkish President Abdullah Gul and Prime Minister Tayyip Erdogan he hoped to strengthen ties with their country and expressed support for Turkey's growing relationship with Iraq, the White House said on Monday.

Obama spoke to the two men by phone earlier in the day.

"In both calls, the leaders discussed a number of current issues, including U.S. support for the growing Turkish-Iraqi relationship, the importance of cooperation in Middle East peace efforts, and the U.S. review on Afghanistan and Pakistan policy," the White House said in a statement.

Turkey has repeatedly attacked hideouts of Kurdish separatists in the northern mountainous region of Iraq.

The White House said Obama emphasized the importance of the U.S.-Turkey alliance and expressed his desire to work on a "broad agenda" of mutual strategic interest.

"The President emphasized his desire to strengthen U.S.-Turkish relations and to work together effectively in NATO," the statement said.

Erdogan's office said the prime minister emphasized the strategic cooperation between the two countries.

"Prime Minister Erdogan especially expressed Turkey's sensitivities on Armenia and the Middle East policies, and he said it was important that the U.S. follows a fair and impartial policy for not hurting relations between the two countries," the statement said.

U.S. objections to Turkish operations against Kurdistan Workers Party (PKK) guerrillas based in northern Iraq have created tensions between Ankara and Washington in the past. The guerrillas have frequently carried out attacks inside Turkey.

U.S.-Armenia ties are another potential source of tension. Turkey firmly rejects allegations of Armenian genocide and has said U.S. recognition of genocide would "poison" U.S.-Turkey relations.

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