AMMAN, Jordan — The United States military must remain in Iraq long enough to ensure that al-Qaida cannot reclaim the havens it has lost there, the U.S. Homeland Security secretary said Monday.

"It's very important to build on the progress that's been made and make sure al-Qaida can't regain ground that it's lost in Iraq," Michael Chertoff told reporters in neighboring Jordan. "Iraq is still a long and difficult process ahead of us."

The Homeland Security chief reiterated U.S. intelligence information disclosed this summer that al-Qaida had "operatives in the pipeline" to "carry out attacks in Europe or the U.S."

Higher vigilance must be maintained, he argued, adding there was no specific imminent threat at hand.

Chertoff was on a three-day visit to Jordan to discuss with U.S. and Jordanian officials the processing and admittance of Iraqi refugees to the United States.

Chertoff said the U.S. would like to see 12,000 Iraqi refugees enter the country this current fiscal year — a jump from less than 2,000 admitted last year — with priority given to those who served alongside U.S. forces in Iraq.

He defended Homeland Security's strict entry measures, which some humanitarian groups say have slowed the process to a trickle.

"The process is actually getting streamlined. It's still always going to be a process that takes a certain amount of time," Chertoff said.

Jordan and Syria shelter the bulk of more than 2 million Iraqi refugees and have complained that the huge numbers were burdening their health and education services.

The U.S. has provided over $200 million in U.N. humanitarian assistance to Iraqi refugees in the Mideast, according to the State Department.