Senior military commanders said Sunday that Iraqi security forces are improving significantly as U.S. officials stood by earlier assessments that some U.S. forces could return home early next year.

The generals played down the fact that the number of top-level battalions of Iraqi soldiers -- those ready to go to war without U.S. assistance -- has fallen from three to one since June.

More important to the mission of training Iraqis is the growing number of Iraqi security forces at all levels, including those able to lead operations with U.S. backing, said Gen. George W. Casey, the commander of multinational forces in Iraq.

"The development of the Iraqi security forces is very much on track," Casey told ABC's "This Week.

He said the goal is to develop Iraqi forces that can operate without U.S. assistance. "You don't build an army to that level overnight ... it's going to be some time for them to get there," Casey said.

Both Casey and Gen. John P. Abizaid, who heads the U.S. Center Command and has overall responsibility for military aspects of the global fight against terrorism, have said U.S. troop levels could decrease in the spring if political and security conditions in Iraq were favorable.

That assessment appeared in question last week when Abizaid and Casey told a Senate committee about the reduction in top-level Iraqi battalions. Some lawmakers expressed concern about the pace and overall success of the training mission.

On Sunday, Abizaid said more Iraqis are in the field at various levels of training and are participating in security operations than before. Field commanders, both U.S. and Iraqi, are confident and remain optimistic that progress is being made, he said.

Iraqi forces already are leading the fight in some areas of the country, Abizaid said, citing parts of downtown Baghdad and southern Iraq as examples. He did not say how long it might take to train enough fully combat-ready Iraqis to replace U.S. troops.

Abizaid also said he was optimistic that the political goals for Iraq would be met. Voting is scheduled for October 15 on a draft constitution, with elections for a new government set for December.

"As long as politics continues to move in the direction that it appears to be moving, and the Iraqi security forces continue to move in the direction that they're moving, the insurgency doesn't have a chance for victory," Abizaid said on NBC's "Meet the Press."

If a legitimate government emerges from elections and represents all of Iraq's political factions, Abizaid said, "there's no reason to suppose that we can't bring force levels down in the spring."

Abizaid also said that the insurgency is "alive and well" even if it is headed for failure.

Casey would not set a specific date for a drawdown of U.S. troops, now numbering nearly 150,000, saying a reduction was part of the overall strategy and would be based on conditions in Iraq.

"It will happen progressively around the country as Iraqi security forces step forward," Casey told CNN's "Late Edition."

Casey said commanders are concerned the war could lose the support of the American public. Recent polls indicate that only one-third of Americans approve of President Bush's handling of the war.

"I think it's important for the American people to understand that we should not be afraid of this fight. This is a tough fight," Casey said. "This is worth it, and we have a plan and a strategy in place that will allow us and our Iraqi colleagues to prevail."

Asked if he worries that the U.S. troops who have died in Iraq -- a number approaching 2,000 -- may have given their lives in vain, Casey said: "No, I don't worry about that. Not yet -- we're not there yet."