Defense Secretary Donald H. Rumsfeld (search) on Tuesday left open the possibility that Turkey's offer to deploy thousands of troops to Iraq -- a move seen just weeks ago as a critical breakthrough for U.S. diplomacy -- could be dropped because of Iraqi opposition.

Turkish officials have indicated in recent days that the proposed deployment, approved by the Turkish Parliament (search) on Oct. 7, could unravel if opposition remains strong.

Asked whether the Bush administration's interest was waning, Rumsfeld suggested that the Turks had set conditions that might not be met.

"What the Turkish government did -- at least my understanding of it -- was they said that under certain circumstances they would be willing to offer forces, subject to finding a method" that satisfied all parties, including their own government and the Iraqi Governing Council (search), he said.

"That process is under way," Rumsfeld added. "Whether it will ultimately find a method of satisfying everybody, I don't know. I hope so because obviously we would like additional forces to be available."

Another senior administration official, speaking on condition of anonymity, said the United States still wants Turkish troops in Iraq but is encountering resistance from the Iraqis.

Iraqi objections are based in part on the views of Iraq's Kurds, who make up about a third of the country's 25 million people. They are sensitive to the legacy of nearly 400 years of Ottoman rule in Iraq.

A 15-year insurgency by Kurdish rebels in Turkey ended in 1999, but the rebels now have bases in northern Iraq and the potential to resume fighting. Turkey fears that Kurds living in an autonomous area of northern Iraq could declare independence, rekindling the insurgency in Turkey.

Turks are mostly Sunni Muslims and their predecessors -- the Ottomans -- favored Iraq's Sunnis, sidelining the Shiite Muslims, now a majority in Iraq.

A large community of ethnic Turks, known as Turkomans, also live in Iraq.

Rumsfeld was careful to note that the U.S. government appreciates the Turkish offer, coming from a longtime U.S. ally whose population strongly opposed the U.S. decision to invade Iraq.

"We certainly appreciate their coming forward as they have," he said.

The administration pushed hard for a Turkish troop contribution in part because it wants an international force to take the place of the U.S. Army's 101st Airborne Division when it completes its scheduled one-year tour of duty in Iraq. It also wants more Muslim troops in Iraq to reinforce the administration's argument that the occupation effort is not purely American.

Rumsfeld said the Bush administration is in discussion with several other countries about possible troop contributions for Iraq, but Turkey is the only one so far to offer large numbers.

A day after the Turkish Parliament's vote to approve the troop deployment, the American-appointed Iraqi Governing Council told L. Paul Bremer, the U.S. civilian administrator in Baghdad, that it opposed a Turkish military presence but was willing to discuss it.

On Saturday, Turkish Prime Minister Recep Tayyip Erdogan said his country was taking into account the view of the Iraqis.

"We aren't longing to send soldiers to Iraq," he was quoted as saying by Turkey's semi-official Anatolia news agency.

"If the Iraqi people say, 'We don't want anybody,' there's nothing else we can do," Erdogan was quoted as saying. "If wanted, we'll go. If not wanted, we won't go. We haven't made a definite decision."

On Monday the prime minister noted that the parliament had already given its blessing.

"But the developments after that authorization became different," he said. "As the Turkish government we fulfilled our responsibility. From now on it is up to them [the Americans]."

Of the 156,000 coalition troops in Iraq, Rumsfeld said 132,000 are American and 24,000 are from other nations, including Britain, Poland and Spain.