BAGHDAD — Iraq’s prime minister signaled Wednesday that he was open to the eventual return of American troops as trainers, underscoring the reality that the United States is likely to be involved in this country’s security even after the last soldiers depart in the coming weeks.

“No doubt, the U.S. forces have a role in providing training of Iraqi forces,” Prime Minister Nuri Kamal al-Maliki said after meeting Vice President Joseph R. Biden Jr., who is here to mark the withdrawal and to inaugurate a new phase in relations between the United States and Iraq.

Mr. Maliki insisted that Iraq could provide for its internal security. And he made much of Iraq’s desire to build a relationship with the United States as a sovereign country, dealing with Washington on the basis of national interest and “mutual respect.”

But his comments suggested that for all the solemn pageantry of a war’s ending, there is likely to be considerable continuity in the security relationship between the United States and Iraq, as it struggles to contain terrorist attacks by insurgent groups.