Rice and Zebari also said a final agreement on the nature of any future U.S. troop presence and Washington-Baghdad relations is close to fruition, but not yet complete.
The two sides had come together on a draft agreement earlier this week, and Rice made an unannounced visit to Baghdad Thursday to press officials there to complete the accord.
"We have agreed that some goals, some aspirational timetables for how that might unfold, are well worth having in such an agreement," Rice told reporters after meeting with Iraqi officials, including Prime Minister Nouri al-Maliki.
A key part of the draft agreement envisions the withdrawal of American forces from Iraq by June 30, 2009.
"This agreement determines the principle provisions, requirements, to regulate the temporary presence and the time horizon, the mission of the U.S. forces," Zebari said.
The pact will allow U.S. forces to stay in Iraq beyond the end of this year, when a U.N. Security Council mandate enacted after the U.S.-led invasion in 2003 expires.
Replacing the U.N. mandate with a formal U.S.-Iraqi pact would give Baghdad direct say over the presence of foreign troops on its soil for the first time since the fall of Saddam Hussein.
There are now about 140,000 U.S. troops in Iraq.
"We are continuing to work to make sure that any timelines that are in the agreement really do reflect what we believe can be done, what's feasible," Rice told reporters on board her plane before her arrival. "Obviously everybody is going to keep an eye on conditions on the ground."
Other issues that need to be tackled include immunity for U.S. troops from Iraqi law and the status of prisoners held by American forces. U.S. forces hold some 21,000 prisoners in Iraq, many of whom have not been charged with a specific crime.
Influential anti-American cleric Moqtada al-Sadr denounced the pact.
"Today, Condoleezza Rice, the occupation foreign secretary, arrived in Iraq to try to put pressure on the government of Iraq to accept terms dictated by the occupation to sign this ominous treaty," Sadr political adviser Liwa Smeism said.
In addition to spelling out that U.S. troops would move out of Iraqi cities by next summer, the Iraqi government has pushed for a specific date - most likely the end of 2011 - by which all U.S. forces would depart the country. In the meantime, the U.S. troops would be positioned on bases in other parts of the country.