(Updates with State Department comment, Pentagon no comment)

WASHINGTON, Oct 9 (Reuters) - The United States cautioned Turkey on Tuesday against making an incursion into northern Iraq after Kurdish rebels launched attacks from there and urged both countries to work together to resolve the conflict.

Turkish Prime Minister Tayyip Erdogan gave the go-ahead on Tuesday for all necessary measures to be taken against Kurdish rebels, including a possible incursion into northern Iraq, after they carried out a series of attacks.

But the U.S. State Department warned against such a move.

"If they have a problem, they need to work together to resolve it and I am not sure that unilateral incursions are the way to go, the way to resolve the issue," said State Department spokesman Sean McCormack.

Asked whether Washington had urged restraint on both sides, McCormack said sovereign states had to make their own decisions about how best to defend themselves.

"We have counseled both in public and private for many, many months the idea that it is important to work cooperatively to resolve this issue," he said.

Both the State Department and the White House said the United States was committed to working with Turkey and Iraq to combat the PKK Kurdish rebel group that has carried out a series of attacks in Turkey.

"It is critically important that all sides involved in this -- the Iraqis, the Turks and certainly we will do our part -- work to combat terrorism. You just can't have these kinds of attacks emanating from Iraq and I think the Iraqis understand that," said McCormack.

White House National Security Council spokesman Gordon Johndroe would not comment specifically on whether the White House would support Turkey authorizing a possible incursion into northern Iraq, where many rebels from the separatist Kurdistan Workers Party, or PKK, are hiding, calling that a hypothetical question.

"Iraq and Turkey want to work together on this problem. The most effective and appropriate way is to protect the citizens of both countries," he said.

Turkish military officials said Kurdish rebels killed 13 Turkish soldiers on Sunday in fighting in Sirnak province, which borders Iraq.

Pentagon spokesman Bryan Whitman declined comment on the latest news from Turkey.

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