WASHINGTON — Under the timetable embraced on Monday by Gen. David H. Petraeus, the number of American combat brigades would decline by one-fourth by next summer, from 20 now to 15 in July, with the prospect of deeper, if as yet unscheduled, reductions to come.

But such a move would raise the question of how the United States can avert an increase in violence in Iraq while carrying out a gradual drawdown. One approach embraced by many lawmakers would be to modify the American mission to emphasize the training and advising of Iraqi security forces so that Iraqis would be pushed into the lead and the vast majority of American combat troops could be quickly withdrawn.

This proposal, which was offered last year by the Iraq Study Group, the bipartisan panel chaired by Lee H. Hamilton and former Secretary of State James A. Baker III, has appealed to many Democrats and some Republicans who are looking to achieve a measure of stability in Iraq while shrinking the role of the American military.

But in his testimony on Monday, Petraeus offered a very different vision. He proposed an American presence that would not only be longer and larger than many Democrats have advocated but would also provide for a greater American combat role in protecting the Iraqi population.

Redefining the American mission to focus primarily on training Iraqi forces and conducting commando raids against terrorists, Petraeus said, would be "premature."

"We have learned before that there is a real danger in handing over tasks to the Iraqi security forces before their capability and local conditions warrant," he added.

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The American commander was not only rebuffing the demand for a firm timeline for withdrawing the bulk of American forces, he was also putting critics on notice that even when reductions come he has a different vision of the manner in which many of the remaining troops would be used.

The general's long-term projection foresaw a diminishing, but still significant, number of American brigades that would continue to assume the primary role in combat operations. By mid-July 2008, when Petreaus anticipates a force of 15 combat brigades, a little over a third of them would be taking the lead in military operations.

A somewhat larger number would be partnered with Iraqi security forces, meaning they would deployed with Iraqi troops while encouraging them to take the lead.

The remainder would be involved in "overwatch," meaning that they would be supporting Iraqi forces and available to come to their assistance but not involved in day-to-day operations to protect the Iraqi public.

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