Odierno provided the update during Obama's meeting with his national security team, which included Vice President Joe Biden, Secretary of State Hillary Clinton, Defense Secretary Robert Gates and other members of the military, intelligence and diplomatic community.
Odierno told Obama the drawdown is on target to be complete by the end of August, White House Press Secretary Robert Gibbs said.
Gibbs told reporters 80,000 troops have already been pulled out and 50,000 remain.
"General Odierno also reported that the security situation has retained the significant improvements made over the last couple of years and that Iraqi security forces are fully prepared to be in the lead when we end our combat mission later this month," Gibbs said.
Odierno told the president the level of violence observed the past two weeks in Iraq has been relatively low but an "uptick" is anticipated in the coming days.
"So the president was satisfied with the progress that we continue to see on the security side ... ," Gibbs said.
"Nothing was brought up with the president that would necessitate us needing to turn back."
Gibbs said it would be "premature" to discuss what it might take to disrupt the plan to have all U.S. ground combat troops out of Iraq by the end of 2011.
Notable deaths of 2014 [PHOTOS]