WASHINGTON —  With Al Qaeda's influence diminishing in Iraq, U.S. troops have much work to do in stemming Iranian support for militias, President Bush's national security adviser said Sunday.

"Iran is very active in the southern part of Iraq. They are training Iraqis in Iran who come into Iraq and attack our forces, Iraqi forces, Iraqi civilians. There are movements of equipment. There's movements of funds," Hadley said. "So we have illegal ... militia in the southern part of the country that really are acting as criminal elements that are oppressing the people down there."

"Al Qaeda, they're on the defensive," he added, citing the illegal militias as a growing threat. The prime minister, Nouri al-Maliki, "decided it was time to take control of the situation down there. ... He's had some success. He's taken control of the port (in Basra). But there's more work to do."

Last week, Defense Secretary Robert Gates said the U.S. will be as aggressive as possible to counter the increase in Iranian support for militias. He said the Iraqis "are in a position themselves to bring some pressures to bear on Iran."

Gates also acknowledged that future troop withdrawals will go more slowly than he had initially hoped last year. He told a Senate panel he expects Gen. David Petraeus, the top military commander in the war, to be able to make an assessment of further drawdowns by mid-September.

On Sunday, Hadley said the Iraqi government has been putting more diplomatic pressure on Iran, which he called a "good thing."

"In addition we will continue to do with Iraqi security forces what we've been doing for some time. We will go after their surrogate operations in Iraq that are killing our forces, killing Iraqi forces," he said. "We will disrupt their networks by which they move fighters, weapons and funds in and around Iraq. And we will cut off as best we can the flow of fighters, weapons and arms into Iraq."

Regarding troop drawdowns, Hadley reiterated that Bush will give Petraeus all the time that he needs to assess the security situation in Iraq.

"What we hope is that conditions on the ground will permit continuation of what we call return on success and more U.S. forces will come out," he said.

Bush "has told them very clearly their only consideration is what they need to do to succeed in Iraq. And his objective is to leave an Iraq in a situation at the end of his term where we have a strategy that is succeeding, that the American people can see progress and hand it over to the next administration whether Republican or Democrat so that they will inherit a strategy ... that is working," Hadley said.

Hadley spoke on "Fox News Sunday."