BAGHDAD - The U.S. military said Sunday that attacks in Iraq linked to Iranian explosive devices have fallen off in recent days after a sharp increase earlier in the month, and that the overall flow of weaponry from Iran has dropped.

The roadside bombs, known as EFPs, are armor-piercing explosives that have killed hundreds of U.S. soldiers in Iraq. U.S. military officials have been saying for months that Iran, a Shiite country, has been supplying EFPs to Shiite militias in Iraq, despite strong denials by Tehran.

"The number of signature weapons that had come from Iran and had been used against coalition and Iraqi forces are down dramatically except for this short uptick in the EPFs in the early part of January," military spokesman Rear Adm. Gregory Smith told a news conference.

"It's uncertain again what is happening in Iran that's leading to that occurrence," Smith said. He added, however, that "we don't think that the level of training has been reduced at all, we don't believe that the level of financing has been reduced."

He said the U.S. is trying to understand the various ways in which Iran exerts influence inside Iraq, including training of and financial support to militias as well as the smuggling of weapons.

Smith's remarks came a week after the top U.S. commander in Iraq, Gen. David Petraeus, said EFP attacks had risen by a factor of two or three recently.

Meanwhile Sunday, a mortar round slammed into the road near a district passport office in eastern Baghdad, killing one civilian and wounding three policemen, officials said.

The attack came a day after at least 19 people were killed in a series of bombings and rocket attacks nationwide. Despite the sporadic violence, hundreds of thousands of Shiite pilgrims commemorated the death of one of their most revered saints in relative peace on Saturday.

While there was no catastrophic attack during Ashoura, Sunni and Shiite militants kept up the steady, although diminished, level of violence that has been chipping away at recent security gains.

People were lining up for the office's 8 a.m. opening and copying documents at nearby stalls when the blast occurred, according to a guard at the scene in the eastern neighborhood of Zayouna.

"While we were organizing those who were coming to get passports, a mortar round landed here," the guard, Haider Hussein, told Associated Press Television News.

The attack left a small crater in the road, and photocopying stalls were pockmarked by shrapnel.

Zayouna, a religiously mixed neighborhood, was the site of a Jan. 1 suicide bombing that killed at least 36 people after the attacker blew himself up in the mourning tent erected for the funeral of a retired Iraqi army officer who himself had been killed in a car bombing.

A relatively uneventful passage of Ashoura had been seen by U.S. and Iraqi officials as a rigorous test of the decline in violence in the country since Washington sent in 30,000 additional troops last year and many Sunni insurgents suddenly joined American forces in the fight against al-Qaida in Iraq.

The 10-day holiday, largely banned by Saddam Hussein and his minority Sunni Muslim regime, commemorates the death of Imam Hussein, grandson of the Prophet Muhammad, in a seventh century battle near Karbala, 50 miles south of Baghdad.

The battle defined the split between Islam's Sunni and Shiite sects.