"We don't expect any change to happen overnight or any hasty change in U.S. policy and commitment toward Iraq," Iraqi Foreign Minister Hoshyar Zebari told Al-Arabiyah TV moments after Obama claimed victory over Republican John McCain.
But he acknowledged that Obama "will not have the same enthusiasm and momentum for this situation" in Iraq as Bush.
The foreign minister said Obama told Iraqi leaders earlier this year during meetings in Baghdad and Washington that "any decision that concerns Iraq would be taken after thorough discussions with the Iraqi government and field military leaders."
Salim Abdullah, spokesman for the largest Sunni parliamentary bloc, agreed.
"We are not concerned that he will take a unilateral decision to move troops quickly from Iraq," Abdullah told The Associated Press.
Some Iraqis, however, are eager to see an end to a U.S. military presence they consider foreign occupation. American officials insist the troops are here to defend the Iraqi people against terrorists.
Salah al-Obeidi, spokesman of anti-American Shiite cleric Muqtada al-Sadr, said Wednesday that with Obama's victory, "we expect that big changes will take place."
The Sadrists are among the most outspoken opponents of the U.S. military presence in Iraq.
Wali Mohammed, a 22-year-old college student in Baqouba, 35 miles northeast of Baghdad, said he wants Obama to stand pat on his campaign pledge to pull the 151,000 U.S. troops out of Iraq.
"We hope Obama will stick to his word," Mohammed said.
Other Iraqis fear their leaders and security forces are not ready to take over and don't want the Americans to leave too soon.
U.S. exit polls showed that only one in 10 American voters called the Iraq war their top concern when making their presidential choice, reflecting expectations Obama will focus more on domestic issues and the economy once he takes over.
Obama's election win comes as U.S. and Iraqi officials scramble to reach a deal on a new security agreement that would end the U.S. military presence in the country by 2012 and give Iraqis a greater role in managing combat operations.
Violence has dropped sharply in the country since Iraqi security forces and the U.S. military gained the upper hand against extremists this spring.
But a string of bombings in Baghdad this week have killed more than 30 people, underscoring that insurgents still pose a threat. And U.S. commanders warn the security gains are reversible.
It remains unclear what impact the Democrat's victory will have on negotiations over the security agreement, but Iyad Jamal-Aldin, a lawmaker from the Iraqiya List, said he doesn't expect it "will speed up the signing of the pact."
Opinions in the run-up to Tuesday's vote differed somewhat in Kurdistan, the generally peaceful three northern provinces where Kurds have enjoyed self-rule since 1991 and have used their ties to Washington to defend their autonomy.
Some Kurdish officials had expressed concern that Obama might not continue the close relationship.
Kurdish lawmaker Mahmoud Othman said Wednesday he thinks the Democrat's administration will usher in a fresh approach from Washington toward the Middle East.
"I think that it's a natural change to take place after a long period with the Republicans in office," said Othman, who praised the Democrat's idea of holding talks with Iraq's neighbor, Iran.
In Baghdad, government spokesman Ali al-Dabbagh said in a statement that Iraq hopes to cooperate with the president-elect to achieve "security and stability in Iraq, to preserve its sovereignty and protect its people's interests."
Associated Press writers Sinan Salaheddin and Hamid Ahmed contributed to this report.