WASHINGTON — General David Petraeus, the top American commander in Iraq, said yesterday that conditions in Iraq might get harder before they get easier and will require “an enormous commitment” over time by America.

Speaking as the Senate debated veto-threatened legislation to start bringing home U.S. forces in October, General Petraeus called the war there “the most complex and challenging I have ever seen.”

The four-star general, named by President Bush to oversee the recent buildup of American forces, cited some progress in the two months since the troop increase began.

Still, he said, “there is vastly more work to be done across the board. … We are just getting started with the new effort.”

He avoided commenting directly on the legislation before the Senate, which passed the House Wednesday night. “I have tried to stay clear of the political minefields of various legislative proposals,” he said.

But his comments made it clear that his war plan did not include a significant reduction of U.S. forces anytime soon.

“This effort may get harder before it gets easier,” General Petraeus told reporters at a Pentagon briefing, depicting the situation as “exceedingly complex and very tough.”

He said the increasing use of roadside bombs and suicide attacks, plus the greater concentration of U.S. troops among the population, has “led to greater U.S. losses” as well as increased Iraqi military casualties.

Asked how many troops he thought would have to remain in Iraq — and for how long — to finish the job, General Petraeus said, “I wouldn’t try to truly anticipate what level might be some years down the road.” However, he noted historical precedents to long U.S. peacekeeping missions.

“It is an endeavor that clearly is going to require enormous commitment and commitment over time, but beyond that time I don’t want to get into try to postulate how many brigades or when we would start to do something,” he said.