Updated

The U.S. military has noted a "significant improvement" in the aim of attackers firing rockets and mortars into the heavily fortified Green Zone in the past three months that it has linked to training in Iran, a top commander said Thursday.

Lt. Gen. Ray Odierno, the top day-to-day U.S. commander in Iraq, also expressed cautious optimism over a decline in the number of American troops killed this month. At least 60 U.S. troops have died so far in July after the death toll topped 100 for the previous three months, according to an Associated Press tally based on military statements.

Odierno said it appeared that casualties had increased as fresh U.S. forces expanded operations into militant strongholds as part of the five-month-old security operation aimed at clamping off violence in the capital, but were going down as the Americans gained control of the areas.

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"We've started to see a slow but gradual reduction in casualties and it continues in July," he said at a joint news conference with Iraqi military commander Maj. Gen. Abboud Qanbar. "It's an initial positive sign, but I would argue we need a bit more time to make an assessment whether it's a true trend."

Odierno's comments came as a car bomb near a market in a predominantly Shiite area in Baghdad killed at least 25 people and the U.S. military said five American troops had died in fighting this week — four northeast of the capital and one in Baghdad.

Smoke billowed into the sky and fires burned on the ground after the thunderous explosion, which occurred as the market in Karradah was packed with shoppers. It also left nine cars burned and set a three-story building on fire, according to police and hospital officials who gave the casualty toll.

It was the deadliest in a series of attacks that left more than 40 people dead nationwide.

AP Television News footage showed columns of smoke rising from two other locations in the area, but it was not immediately clear what caused them.

The three U.S. Marines and a sailor died Tuesday while conducting combat operations in Diyala province — the site of a major military operation against a Sunni insurgent stronghold, the military said. Another U.S. soldier was killed Wednesday during a gunbattle in southern Baghdad.

A Marine also died Sunday in a non-combat related incident in Anbar province, west of Baghdad, the military said separately.

Faris Hamza, a 42-year-old who works in a clothing store near the site of the explosion in Baghdad, said the market was packed with shoppers. He described a scene of chaos with vendors helping to carry the wounded to hospitals and wounded women and children begging for help.

"The stalls were turned upside down because of the powerful explosion. There were many shoppers in the market and most of the store owners were looking forward to good sales a good sales but instead they had to close their shops and run away," he said, his shirt soaked with blood. "This violence is not only killing people, it is also starving them."

In northern Iraq, a car parked near a popular restaurant in the center of the oil-rich city of Kirkuk, killing at least six civilians and wounding 25, police Brig. Gen. Sarhat Qadir said.

A homicide bomber blew himself up at the gate of a police station some 50 miles west of the northern city of Mosul, killing at least six people and wounding 13, police Brig. Gen. Mohammed al-Waqaa said, adding that those most of the casualties were policemen.

South of Baghdad, a police patrol south was struck by a roadside bomb, killing five officers and wounding two as they were on their way home to Hillah from an operation with U.S. forces in Diwaniyah, police said.

A former aide to Iraq's top Shiite cleric also was killed in a drive-by shooting in the holy city of Najaf south of Baghdad, security officials said. Kazim Jabir al-Bidairi was the third person linked to Grand Ayatollah Ali al-Sistani to be killed in two months.

In Baghdad, debris was swept up from two homicide bombings that killed at least 50 cheering, dancing, flag-waving Iraqis celebrating the national soccer team's semifinal victory in the Asian Cup tournament.

The attacks bore the hallmarks of Sunni militants who have fueled the violence tearing at the fragile fabric of Iraq for nearly four years. But these bombings, in parked cars less than an hour apart in separate corners of Baghdad, appeared designed to gain attention rather than target a particular sect.

Salim Jabour, a retired government employee, said he would defy fears of more violence and watch Sunday's final against Saudi Arabia in a coffee shop instead of huddling at home.

"We will not allow terrorists to steal the opportunity to express happiness from the Iraqi people," Jabour said.

Odierno said networks continue to smuggle powerful roadside bombs and mortars across the border from Iran despite Tehran's assertions that it supports stability in Iraq.

His remarks came two days after the U.S. and Iranian ambassadors to Iraq met in Baghdad and agreed to establish a security committee to jointly address the violence amid Washington's allegations that Tehran is fueling the violence by support Shiite militias. Odierno said the military also believes training of extremists is being conducted in Iran.

Iraqi government advisers said Thursday that the details of the committee had been worked out and the panel would have its first meeting on Saturday. A senior aide to Prime Minister Nouri al-Maliki, Sami al-Askari, said the committee will be chaired by Iraq but he could not provide details about the composition of the other delegations.

"One of the reasons why we're sitting down with the Iranian government ... is trying to solve some of these problems," Odierno said at a news conference in the Green Zone, which is home to the U.S. Embassy and the Iraqi government headquarters.

"We have seen in the last three months a significant improvement in the capability of mortarmen and rocketeers to provide accurate fires into the Green Zone and other places and we think this is directly related to training that is conducted in Iran," Odierno said, without offering any proof. "So we continue to go after these networks with the Iraqi security forces."

Attacks against the sprawling complex along the Tigris River in the center of Baghdad have increased in recent months, adding to the concern over the safety of key Iraqi and international officials and thousands of U.S. soldiers and contractors who live and work there.

On July 10, a barrage of more than a dozen mortars or rockets struck the area, killing at least three people, including an American, and wounding 18. In a report last month, the United Nations office in Baghdad said the "threat of indirect fire" — meaning rockets and mortars — into the Green Zone had increased, adding that the barrages had become "increasingly concentrated and accurate."

Iran has denied the U.S. allegations about its activities in Iraq.

Complete coverage is available in FOXNews.com's Iraq Center.