BAGHDAD — The American 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 yesterday.

The top day-to-day American commander in Iraq, Lieutenant General Ray Odierno, also expressed cautious optimism over a decline in the number of American troops killed this month. At least 60 American troops have died so far in July after the death toll topped 100 for the previous three months.

General Odierno said it appeared that casualties had increased as fresh American 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.

“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 the Iraqi military commander, Major General 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.”

General 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.

“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,” he said.