NATO leaders also approved expansion of peacekeeping in Afghanistan, raising troop levels to 10,000, and agreed to end their mission in Bosnia by the end of the year and turn over responsibility for peacekeeping to a European Union force.
CBS News Correspondent Mark Knoller reports that before the early handover of sovereignty was announced, President Bush and Prime Minister Tony Blair showed signs of getting the news.
After getting a heads-up from smiling Defense Secretary Donald Rumsfeld seated behind him, Mr. Bush was seen checking his watch, whispering a few words to Blair and then shaking hands with him.
The move is something of a vindication for Mr. Bush and Blair — the leaders who led the coalition that ousted Saddam Hussein — although the security situation remains unsettled.
"We will challenge these elements in Iraq, the antidemocratic elements, by even bringing the handover of sovereignty before June 30 as a sign we are ready for it," Iraq's interim Foreign Minster Hoshyar Zebari said after meeting Blair on the margin of the NATO meeting.
The number of NATO instructors to be deployed and the timing of the operation were unclear, but the move will give NATO a military presence on the ground in Iraq for the first time. Sixteen nations have sent troops individually to join coalition forces in Iraq.
A statement called on alliance officials to "urgently" discuss details of the training plan with the Iraqi authorities. NATO said it would also urgently consider "further proposals to support the nascent Iraqi security institutions."
"We have shown that were are firmly resolved to confront risks and threats to our security well beyond NATO's traditional zone of operation," said alliance Secretary General Jaap de Hoop Scheffer.
However, the decision falls well short of U.S. hopes that NATO would assume a major military role in Iraq, perhaps by taking over the multinational-division currently run by Poland.
Opposition from France and Germany has ensured that NATO won't deploy large numbers of troops and differences persist between those nations and the United States over the implementation of the training program.
While Washington foresees a significant NATO involvement, including the setting up of an alliance command in Iraq, Paris and Berlin prefer a lower profile operation, with NATO coordinating national training programs.
Alliance plans for a bigger role in Afghanistan are well behind schedule because nations have been reluctant to provide necessary troops and equipment. NATO's peacekeeping mission in Afghanistan is currently limited to 6,400 troops in the capital, Kabul, and the northern city of Kunduz.
Afghan President Hamid Karzai has long urged a wider NATO role and is expected to attend the summit Tuesday.
The summit is also set to offer a new program of defense cooperation to Middle Eastern nations and set up permanent NATO diplomatic missions in Central Asia and the Caucasus.
Mr. Bush declared Sunday in Turkey that the alliance was poised to "meet the threats of the 21st century."
With Mr. Bush in town and NATO leaders gathering, Turkish security forces sealed off a large sections of Istanbul amid fears of terrorist attacks and violent protests. Fighter planes flew overhead and 23,000 police and security forces patrolled the streets.
Earlier Sunday, Mr. Bush sought to strengthen ties with vital ally Turkey, a task complicated by threats from Iraqi militants to decapitate three Turks unless the country's companies stop aiding U.S. forces in Iraq.
Turks overwhelmingly opposed the war in Iraq. Mr. Bush, who arrived in the country Saturday, is widely unpopular here — more than 40,000 Turks turned out for a peaceful protest Sunday against his visit and the NATO summit.
On Monday, police used tear gas to stop hundreds of protesters from approaching the conference center where NATO leaders were meeting in Istanbul.
The protesters threw fire-bombs and several police and protesters were injured and were evacuated to local hospitals.
Mr. Bush's arrival in Turkey was preceded by a series of bomb blasts, including one Thursday that injured three people outside the Ankara hotel where Mr. Bush was scheduled to stay. Another blast the same day on an Istanbul bus killed four people and injured 14.
The bombings has been blamed on militant leftists.