According to the White House statement, the troop withdrawals are one of several "aspirational goals" which will be implemented depending on conditions on the ground.
Those goals include "the resumption of Iraqi security control in their cities and provinces and the further reduction of US combat forces from Iraq," Perino said.
Washington says an agreement is needed to lay out the ground rules for US forces in Iraq after the UN mandate for their presence expires at year's end, but negotiations have run into trouble, particularly over whether US troops would be immune from Iraqi prosecution.
However, there appeared to be some confusion over whether the agreement would lead to the US quitting Iraq entirely.
While the White House referred only to reducing troop levels, Ali al-Dabbagh, Iraq's government spokesman, said that the aim of the agreement was "to decrease the number of American forces in Iraq and later withdraw them".
Perino said US forces would move "from a primary combat role" to what Washington calls an "overwatch role" of training and advising Iraqi forces, and carrying out special forces operations.
"This transition and the subsequent reduction in US forces from Iraq is a testament to the improving capacity of Iraq's Security Forces and the success of joint operations" begun in January 2007, she said.
The US military says that violence across Iraq has fallen to a four-year low.
US-led forces have transferred security in 10 of the country's 18 provinces to Iraqi forces, the most recent being in Diwaniya province on Wednesday.
Iraqi leaders believe that they can take over security responsibilities in the remaining eight provinces by the end of this year.
Bush and al-Maliki had aimed to confirm an agreement by July 31, but on Friday the White House spokeswoman said the two leaders had "agreed on a common way forward to conclude these negotiations as soon as possible".
A US embassy official in Baghdad said on Friday that the originally envisaged security pact called the Status of Forces Agreement (SOFA) had now been "suspended".
"The SOFA as we had in Japan or Germany has been suspended or put aside but not thrown away," he told the AFP news agency.
He also said the two sides are currently negotiating a "security protocol or operational protocol" that contains the key contents of the SOFA but would be for a "certain period of time".