WASHINGTON - The United States and Iraq have agreed to set a "general time horizon" for the "further reduction of U.S. combat forces in Iraq" following the improvement in security conditions in the country, the White House said Friday. The breakthrough, which was reached between President George W. Bush and Iraqi Prime Minister Nuri Kamal al-Maliki in discussions via video link on Thursday, could lead to the successful completion of a long-term security agreement covering American operations in Iraq " from combat missions to detaining Iraqis " by the end of this month, The New York Times said, citing an unnamed White House official. "We're converging on an agreement," the official said, referring to ongoing negotiations between Iraq and the United States on the deal. The long-term agreement had been held up by differences over issues like the extent of Iraqi control over American military operations, the right of American soldiers to detain suspects without the approval of Iraqi authorities and Iraqi demands for a timetable for withdrawal. But in a statement, the White House said Bush and Maliki had agreed "that improving conditions should allow for the agreements now under negotiation to include a general time horizon for meeting aspirational goals " such as the resumption of Iraqi security control in their cities and provinces and the further reduction of U.S. combat forces from Iraq." The White House offered no specific dates for troop cuts, but the inclusion of even just a reference to a time horizon is a significant concession by the Bush administration, which has long resisted setting a timetable for cuts in combat forces. It is a tacit admission that the United States' military presence in Iraq is not endless. The administration on Friday insisted that it had not shifted its position. It said that the move was simply a reflection of the changing nature of conditions in Iraq. "These are aspirational goals, not artificial timetables based on political expediency," said Scott Stanzel, a White House spokesman, who was traveling with the pesident in Tucson, Arizona, where Bush was attending a fund raiser. The Democrats, including Senator Barack Obama, the presumptive Democratic nominee for president, have long pushed for a specific timetable for troop withdrawals. Obama's Republican rival, Senator John McCain of Arizona, on Friday said the agreement was evidence that the addition of tens of thousands of combat troops to Iraq last year " the so-called surge, which he supported from the start " had worked. "Withdrawal is possible because of a successful surge strategy that senator Obama opposed, campaigned against, railed against during the process of running for the Democratic nomination and now, fortunately for everyone, he will enjoy the benefits of that successful strategy," said Nicolle Wallace, a spokeswoman for McCain. In the statement, the White House insisted there would not be "an arbitrary date for withdrawal," and again reiterated what has been Mr. Bush long-standing opposition to what he has called "an artificial timetable for withdrawal." The United States and Iraq have been trying to negotiate a long-term security agreement that would clear the way for American troops to operate in Iraq after a United Nations mandate expires at the end of the year. But the negotiations have been deadlocked. Recently, American officials had said they were no longer optimistic that a comprehensive, long-term agreement could be reached by the year's end. There now appears to be movement toward a deal, and the Bush administration seems comfortable in the negotiations about discussing handing over greater security control to the Iraqi army. "We are just where we want to be" in the negotiations, Stanzel told reporters. However, a deal seems in reach by the end of this month only if dates for a specific timetable for troop reductions and other specific legal details governing military forces, known as a Status of Forces Agreement, are left to future talks. The negotiations have been complicated by political currents in both countries. U.S.-backed Iraqi officials facing elections in the fall do not want to be seen as capitulating to Washington. At the same time, they are eager for some form of agreement to prevent any rapid departure of American forces. In the United States, Bush has pushed hard for a deal to be completed by July 31. But Democrats in Congress are reluctant to sign off on an agreement before the presidential elections, and Republicans are divided on the issue.