President Barack Obama says the US and Iraq will enjoy a "normal relationship between sovereign nations" after US troops leave at the end of 2011.
He met Iraqi Prime Minister Nouri Maliki in Washington for talks on Iraq's future as American troops prepare to complete their withdrawal.
They laid wreaths at a military cemetery where many of the almost 4,500 Americans killed in Iraq are buried.
Mr Obama confirmed no bases or troops would remain in the country next year.
"Those days are over," Mr Obama said, adding that Iraq's sovereignty should be respected.
There are concerns in the US over the level of Iranian influence within Iraq, notably within the Shia-dominated government led by Mr Maliki.
It is a delicate issue for Mr Maliki, who essentially owes his position to Iran's support, says the BBC's Jim Muir in Baghdad.
But Mr Obama said he was not concerned about Iraq coming under Iran's sway, including its stand on Syrian President Bashar al-Assad.
"Even if there are tactical disagreements I have no doubt those decisions are made based on what's best for Iraq, not considerations of what Iran would like to see," he said.
Speaking at the White House, both Mr Obama and Mr Maliki expressed their expectation that their countries would continue to have a broad relationship and an "equal partnership".
"As we end this war, and Iraq looks to the future, the Iraqi people must know you do not stand alone," Mr Obama told Mr Maliki.
Mr Maliki said the US withdrawal "indicates success, not like others have said" and that the two countries had completed "the first page of constructive co-operation".
Outside interference in Iraq would not be allowed, he added, but he said Baghdad would need to co-operate with the US and required information-sharing, training and military equipment in order to ensure security.
Regional subtleties remain, though: Mr Maliki's government has taken a different stance on Syria than the US, one seen as closer in line to Iran's views.
While the US has called for Syrian President Bashar al-Assad to step down, Mr Maliki has warned of a civil war if Mr Assad leaves. Iraq also abstained from an Arab League vote that imposed sanctions on Syria.
'Blood and treasure'
Later, President Obama and Prime Minister Maliki jointly placed a wreath at the Tomb of the Unknowns at Arlington National Cemetery, near Washington DC.
The two leaders stood solemnly as the national anthems of the US and Iraq played, and service members stood to attention while a bugler played.
The high-level visit comes as Iraq prepares to take responsibility for its security as US forces leave after eight years.
Speaking alongside Mr Obama at a White House news conference, Mr Maliki appeared confident that the handover of security responsibility to Iraq has been successful so far.
"Nobody imagined we would succeed in defeating terrorism and al-Qaeda," he said.
The question of the US arming Iraq's military remains, with Mr Maliki saying his government has "raised the issue".
Mr Obama indicated he hoped the US would carry out joint military exercises with Iraq, but said first: "We've got to train their pilots".
The US has sold Iraq F-16s fighter jets and Mr Obama noted that Iraq needed an effective Iraqi air force.
Iraqi leaders admit they still need help to meet any threat to their borders and airspace.
Talks had been expected to include whether US troops can return to assist Iraqi forces, and the fate of a US detainee, but both leaders skirted the issue, saying only that the US military operation was coming to an end.
Troops are due to complete their pullout by the end of the year, and no agreement has been reached that will allow American forces to return if required.
The US will retain influence, with a strong diplomatic presence and 150 military trainers in Iraq.
"We've got an enormous investment of blood and treasure in Iraq," Mr Obama said.
"And we want to make sure that even as we bring the last troops out, that it's well understood, both in Iraq and here in the United States, that our commitment to Iraq's success is going to be enduring."
The Pentagon had wanted legal assurance that US troops would not face prosecution under Iraqi law, something Baghdad was unable to provide, paving the way for the full withdrawal now under way.
Meanwhile, Nato has also decided to withdraw its Iraq training mission by the end of the year after Baghdad also refused to give it legal immunity.
In an echo of the US-Iraq negotiations, Nato was unable to agree a deal with Iraqi officials despite several weeks of "robust negotiations", Nato Secretary General Anders Fogh Rasmussen said.