House Republicans and Democrats agreed Thursday to dismantle the Immigration and Naturalization Service, which has come under intense criticism since the Sept. 11 attacks.

Under their plan, the INS would be replaced by separate bureaus for enforcement of immigration law and for providing immigration services. The bureaus would report to an assistant attorney general for immigration affairs, who would be the No. 3 official in the Justice Department.

"This agreement will allow Republicans and Democrats in Congress, in concert with the Bush administration, to work together on fundamentally dismantling the INS," said Rep. James Sensenbrenner, who chairs the House Judiciary Committee, which has oversight of the INS.

The plan combines two bills, one sponsored by Sensenbrenner, R-Wis., and Rep. George Gekas, R-Pa.; the other by Michigan Rep. John Conyers, the Judiciary Committee's senior Democrat, and Rep. Sheila Jackson Lee, D-Texas.

"We want this to be a comprehensive response to the disaster of immigration affairs," Lee said.

The INS has been criticized for years because of long backlogs of applications for benefits such as naturalization or permanent residency. INS supporters and critics say the agency is burdened with conflicting missions to help immigrants enter and stay in the country and to identify and keep out those who try to enter illegally or who may pose a danger.

The terror attacks exposed some of the agency's deficiencies in tracking foreign visitors. Attorney General John Ashcroft said the attacks added new urgency to INS restructuring, and Commissioner James Ziglar set out to create clearer divisions between INS benefits and enforcement duties while keeping the agency intact.

Pressure for more sweeping change intensified in the last two weeks after student visa paperwork for two Sept. 11 hijackers were delivered to a Florida flight school six months after the attacks. President Bush said he was "plenty hot" after learning of the blunder, and this week his domestic security team recommended the INS and Customs Service be merged to create a single border control agency.

White House spokesman Taylor Gross said Bush agrees major change is needed and will work with Congress.

Sen. Edward M. Kennedy, D-Mass., is preparing to introduce INS reform legislation in the Senate. His bill would split the INS into two agencies. Rather than an assistant attorney general in the Justice Department, Kennedy wants an independent administrator appointed by the president to oversee the separate immigration bureaus.

"This is not the time to diminish the authority of the person running the nation's immigration agency," said Stephanie Cutter, Kennedy's spokeswoman. "We need to maintain strong overall leadership to ensure uniformity and decisive action in a crisis. The House legislation does not provide for that leadership."