WASHINGTON — Military officials accused Iran today of posing a long-term threat to Iraq by training and arming insurgents there, while American lawmakers said they were disappointed that Baghdad opened up its doors to the Islamic Republic’s top leader.

“I think it’s offensive,” Senator Levin, Democrat of Michigan, said of President Ahmadinejad’s two-day trip to Iraq this week.

Iraq has “got every right to invite whomever they want. They’re sovereign. But we have a right to express an opinion about it,” Mr. Levin, chairman of the Senate Armed Services Committee, said.

Mr. Levin’s remarks come as America is struggling to combat Iran’s growing influence in the region, and senior military commanders say it is providing powerful bombs to Shiite militias in Iraq.

“We have no doubt they are still supporting insurgents,” the former no. 2 military commander in Iraq, Lieutenant General Ray Odierno, said at a Pentagon press conference. Asked if that was the greatest threat to stability in Iraq, he said, “If you ask me what I worry about most, I do worry about that as a long-term threat. And I think we have to, you know, constantly watch it.”

General Odierno, who has been nominated for a fourth star and assignment as vice chief of staff of the Army, said it was not surprising that there were fewer attacks during Mr. Ahmadinejad’s visit to Baghdad, since it is mainly Iranian-backed Shiite military members who have been conducting rocket and other attacks in the capital.

The top commander of troops in the Middle East, Admiral William Fallon, echoed these remarks in a Senate hearing at which he said Iran was fanning the flames of global terrorism.

While Mr. Ahmadinejad has denied charges of harmful meddling in Iraq, “the facts prove otherwise,” Admiral Fallon told the Senate Armed Services Committee.

Mr. Ahmadinejad’s visit to Iraq marked the first by an Iranian leader since the country’s 1979 Islamic Revolution. During his trip, he insisted American power is crippling the region and portrayed himself as the enduring partner of Baghdad’s Shiite-led government.

America has no diplomatic ties with Iran because it regards the country as a state sponsor of terror. But recognizing its influence on Iraq stability, officials last year opened limited discussions with Iranian officials by demanding the country stop arming Shiite militias.

Admiral Fallon called Mr. Ahmadinejad’s visit a “mixed bag” because it presented an opportunity for Baghdad to push Mr. Ahmadinejad directly to stop the flow of weapons and start working with coalition forces.

“From our perspective, we are not going to help resolve the problems inside that country without assistance from outside,” he said.

But several lawmakers on the panel said they saw Baghdad’s invitation as a grave mistake and said Iran deserves only to be isolated.

“I would hope that others in the administration would express their indignation about this visit and the comments made by that president because they go to the very heart of the enormity of the sacrifices of life and limb that we have suffered in trying to provide Iraq the ability to become a strong and sovereign nation,” the committee’s no. 2 Republican, Senator Warner, said.

More broadly on Iraq, General Odierno and Admiral Fallon said they were encouraged at prospects for further progress even as America reduces its troop levels over the next few months.

“I think there should be little doubt that our desire is to continue to bring our force levels down, as the Iraqis demonstrate their ability to stand up and take responsibility for security in the country,” Admiral Fallon said. “Those trends are certainly encouraging and moving in the right direction. But it’s critical that we don’t lose the ground that’s been so hard fought.”

Admiral Fallon said officials will probably need some time this summer to reassess the situation before drawing down more troops.

By July, the Pentagon is on track to complete its reduction from 20 to 15 active-duty brigades deployed to Iraq. The top commander in Iraq, General David Petraeus, was expected to ask President Bush to wait until as late as September to decide whether to bring home more troops.

Admiral Fallon cautioned that any specific timeline is purely speculation at this point.

“Nothing is written in stone,” he said.

General Odierno spoke hopefully of an apparent change of direction by a radical Shiite cleric, Muqtada al-Sadr, and his Mahdi Army, which has posed some of the biggest challenges to American efforts to stabilize the country.

“I think he’s trying to move them away from a militia-based organization to one that is more — as it started out to be — helping the poor Shiite community have a role and a vote in what goes on in the government of Iraq,” General Odierno said. “I think I see him trying to move toward that.”

He said this is encouraging in the sense that the majority of the Mahdi Army is “becoming more reconcilable” with the central government and its efforts to develop a Sunni-Shiite power sharing arrangement.

Rogue elements of the Mahdi Army are being supported by Iran and are now splitting off from Mr. al-Sadr’s main movement, the general said. “That’s actually helpful for us because we now understand who’s doing what.”