(CNN) -- President Bush and Iraqi Prime Minister Nuri al-Maliki have agreed to include a "general time horizon" for meeting goals such as reducing U.S. combat forces and transferring Iraqi security control across the country, the White House said Friday.
The two men "agreed that the goals would be based on continued improving conditions on the ground and not an arbitrary date for withdrawal," the White House said in a statement.
The discussion follows a drop in violence in Iraq, improvements in the performance of the Iraqi security forces, and subsequent calls from Iraqis for the United States to formulate a troop withdrawal timetable.
It also came as a suicide truck bomber in northern Iraq attacked an Iraqi army patrol on Friday, killing three soldiers and wounding seven others, an Interior Ministry official said.
The incident -- in Flifla, east of Mosul in Nineveh province -- is the latest strike in the northern region, where al Qaeda in Iraq maintains a strong presence and violence continues to flare in a country that is enjoying a decrease in fighting.
The White House statement stemmed from a conversation between Bush and al-Maliki by closed-circuit television Thursday -- the latest in their regularly scheduled video conferences. Al-Maliki's office also released a statement on the conversation.
Iraqi government spokesman Ali al-Dabbagh said both sides are focused "on determining a horizon time for achieving a complete handover of the security responsibilities."
The White House statement said they "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."
Bush and al-Maliki also discussed ongoing negotiations to establish a normalized relationship between the two countries.
The two leaders said progress was being made on areas of cooperation including economics, diplomacy, health, culture, education, and security, the White House said.
They also discussed the improving security situation and the performance of Iraqi security forces the visit to Iraq last week by Turkey Prime Minister Recep Tayyip Erdogan, al-Maliki's recent visit to the United Arab Emirates, and investment initiatives.
The White House said the men discussed the return to the United States of the final "surge" brigade and the "ongoing transition from a primary combat role for U.S. forces to an overwatch role." That involves training and advising and performing counterterror operations.
Iraq's security environment has dramatically improved by all accounts.
One factor is al-Maliki's major military offensives this year against Shiite militants in Basra, Amara and Baghdad's Sadr City and Sunni insurgents in Nineveh province.
Security control has been transferred from the coalition to Iraq in 10 of the country's 18 provinces, and another handover is expected in the coming weeks in Anbar province.
Security has been the most contentious item as the United States and Iraq have negotiated the agreements that will set the parameters of their bilateral relationship.
The U.S. military presence is spelled out by a U.N. mandate, but that is due to expire by the end of the year.
Iraq and the United States want to replace that mandate with a bilateral status of forces agreement, or SOFA, spelling out how U.S. troops operate.
The U.S. and Iraqi governments were hoping to come up with a deal by the end of this month. Now they believe they might have to settle for signing a temporary operating protocol because it could take some time to reach a longer-term status of forces agreement.
The two sides also are negotiating a strategic framework agreement to address all aspects of the bilateral relationship.
Iraqi spokesman al-Dabbagh said the eventual complete handover of security would pave the way for withdrawing U.S. troops.
"The two sides will work to increase the efficiency and effectiveness of Iraqi forces and to improve the security situation on the ground to achieve this goal," he said.
As for a transition from combat to training and advising, al-Dabbagh said such a role for U.S. troops remaining in Iraq would be "for a limited period of time because of the significant improvement in building the Iraqi forces and the successes achieved by the joint cooperation between Iraqi forces and Multi-National Forces."