WASHINGTON (CNN) -- The White House said Monday it is in "constant dialogue" with Iraq and Turkey about the Turkish military operation against Kurdish rebels in northern Iraq.
Turkey said Monday 41 militants and two military personnel died in a further day of fighting.
Lt. Gen. Carter Ham, the director of operations for the U.S. Joint Chiefs of Staff, said the Turkish push did not appear to be "winding down" Monday, "but it does very clearly appear to be limited."
"It appears to be what the Turkish military forces said they would do, of limited depth and of limited duration. We've seen nothing to contradict that so far," Ham told reporters at the Pentagon.
White House spokeswoman Dana Perino said: "The Iraqis are talking with the Turks, and we think that type of dialogue is important. We are in constant dialogue to make sure this is handled in a way that is narrowly targeted to hit the PKK, to limit or hopefully cause no civilian casualties."
The Kurdistan Workers' Party, or PKK, has spent two decades fighting for autonomy for Kurds in southeastern Turkey, with some of its attacks launched from inside northern Iraq.
Turks regard the PKK as terrorists and point to indiscriminate PKK attacks against civilians as well as police and military targets over the years.
Turkey has been taking cross-border military action against the PKK since the group launched attacks last fall on targets in Turkey from bases in Iraq's Kurdish region.
Turkish forces, backed by the air force, began a ground operation last Thursday night against Kurdish rebels in northern Iraq -- the first significant Turkish ground offensive into Iraq since the fall of Saddam Hussein's regime.
While the United States is supportive of Turkey's efforts to fight terror, it is concerned that it might generate regional instability.
Turkish troops in northern Iraq were working to take over rebel strongholds and hideouts and render them useless, and to disrupt logistical supply lines.
Turkey's military said Monday that 41 more rebels were killed in the fighting, bringing the militant death toll in its operation to 153. Two more military fatalities were report, bringing that total to 17.
Perino, speaking at an off-camera but on-the-record gaggle with reporters, was asked if the situation has gotten better or worse.
"I don't know if it's worse or better," she said. "It's not an ideal situation. The ideal situation is that the PKK wouldn't exist in Iraq."
Perino said the U.S. government is in contact with Turks "on a variety of levels."
"The PKK is a common enemy of Turkey and the United States, and Iraq is a fragile state as an emerging democracy. It's concerned about what is going on," she said.
Turkey has not indicated how long the campaign will last.
Speaking in Canberra, Australia, on Sunday, Defense Secretary Robert Gates said he hopes the operation "would be short" and "precise." He said he hopes civilian casualties will be avoided and that the Turkish troops will "leave as quickly as they can accomplish their mission."
Gates said Turkey needs more than military action to deal with the problems involving the Kurds and the PKK and called it a "difficult, long-term problem."
"I think that all of our experience in Iraq and Afghanistan shows us that, while dealing with a terrorist problem does require security operations, it also requires economic and political initiatives," Gates said.
Iraq's government on Sunday called on Turkey to withdraw its forces "as soon as possible," according to a statement released by government spokesman Ali al-Dabbagh.
"The Turkish incursion is a direct threat to the peace and stability in the region," the statement said. Iraqi officials discussed the Turkish military incursion at national security meeting in Baghdad on Sunday.
Nechirvan Barzani, prime minister of Iraq's Kurdish Regional Government, on Sunday expressed his concerns about the operation, which he said is targeting "civilian infrastructure." During remarks in Irbil, he emphasized the importance of political solutions.
"In the 1990s Turkey, at times with our help, tried to solve the problem of the PKK militarily and today they are trying again. But our experience clearly shows that military methods cannot be successful. I am ready to go to Ankara at any point. Four-party talks between Washington, Istanbul, Baghdad, and Irbil will help find a long-lasting and peaceful solution to this problem. " E-mail to a friend
Journalist Andrew Finkel contributed to this report