The quantity of Iranian bomb-making components being found in Iraq is increasing despite a fall in attacks and 20 Iranian-trained agents are still operating south of Baghdad, a top U.S. general said on Sunday.

Extensive Iranian influence in Iraq remained evident, said Major-General Rick Lynch, despite signs of a possible easing of tensions between Washington and Tehran over security in Iraq.

Iranian influence is dominant at many levels, said Lynch, whose area of command extends from Baghdad's southern suburbs south through Sunni Arab insurgent strongholds to the major Shi'ite cities of Kerbala and Najaf.

Lynch said his troops were chasing 20 targets he identified as Iraqi Shi'ites who were agents for the Iranian Revolutionary Guards Corps's (IRGC) elite Qods Force.

They were trained in Iran and they're conducting operations in our battle space, Lynch told reporters. They're Iraqis but they're IRGC surrogates and they're still out there.

Lynch said in August that military intelligence suggested there were about 50 IRGC troops in southern Iraq training Shi'ite militias in the use of mortars and rockets.

His latest comments came despite an apparent softening of rhetoric by U.S. officials in Baghdad towards Iran.

Washington accuses Tehran of arming, training and funding Shi'ite militias in Iraq, charges Iran denies, but U.S. ambassador to Iraq Ryan Crocker late last month noted several positive developments in Iran's involvement in Iraq.

These included a sharp drop in mortar attacks on Baghdad's heavily fortified Green Zone, many blamed on Shi'ite militias using Iranian weapons, and the Mehdi Army militia ceasefire ordered in August by Shi'ite cleric Moqtada al-Sadr.

On Friday, the U.S. military released nine Iranians, including two it accused of links to the Qods Force.

Falls in U.S. military and Iraqi civilian casualties in the past two months have been attributed to a surge of 30,000 extra U.S. troops, which was completed in mid-June, and tribal sheikhs organizing concerned citizens into local police units.

Lynch said there had been a 59 percent fall in roadside bomb attacks in his area including explosively formed penetrators -- arming-piercing bombs known as EFPs -- since July 1.

The number of EFP attacks are on the decline but the number of EFP munitions we're finding has indeed increased, he said.

We've come across weapons caches with large numbers of EFP components all traceable back to Iran based on tool markings.

Lynch said he did not know whether these components were being found more often because more were coming in or whether his troops were conducting more searches.

He said he was also troubled by the number of Iranian rockets being found. In two recent cases, he said, 46 Iranian rockets were found ready and aimed at a U.S. operating base and several more were discovered near a U.S. patrol post.

(Editing by Matthew Tostevin)