Despite calls to tighten the country's immigration laws following the September terror attacks, House leaders on Tuesday pushed through a bill that would allow some illegal immigrants to stay in the country while their residency paperwork is being processed.

But in a move that might dim the bill's chances in the Senate, they attached a border security bill in hopes that the combined bill would get by Sen. Robert Byrd, D-W.Va.

The combined bill was approved on a 275-137 vote by the House.

Byrd has been blocking the border security bill in the Senate, saying senators should have a chance to debate and amend the bill before voting on it. A combined immigration-border security bill would fare no better with Byrd, spokesman Tom Gavin said Tuesday.

President Bush, who wants to present Mexican President Vicente Fox with an immigration agreement when he visits him this month, is squarely behind the bill.

The border security bill would boost the pay of border patrol agents and allow the Immigration and Naturalization Service to hire 200 new investigators and another 200 inspectors.

It also would require the INS to establish a foreign student tracking system that records the acceptance of aliens by educational institutions, the issuance of student visas and the enrollment of aliens at schools. Several of the hijackers involved in the Sept. 11 attacks were in the country on student visas.

The bill would also require that passports issued after 2003 be tamper-resistant and that visitor documents be machine-readable with biometrics, such as face recognition technology.

"I applaud the House for working in a bipartisan fashion to pass legislation that strengthens border security while recognizing the importance of keeping families together and making America a more welcome society," Bush said Tuesday night.

House Majority Leader Dick Armey, R-Texas, said the bill will "make our borders more secure from illegal immigration" and "be more humane and effective in handling ... the paperwork on people who do come here in compliance with our laws."

The immigration portion of the bill would extend a deadline for giving hundreds of thousands of illegal immigrants the chance to apply for residency without leaving the United States. Many of those immigrants are here on work visas that have expired, but they did not leave the country, officials said.

More than 600,000 illegal immigrants were eligible under the Legal Immigration and Family Equity Act to apply for visas without leaving the country, but it expired last April.

Under the House bill, the program would be extended to Nov. 30, or four months after the regulations are issued, whichever comes first.

A reinstated program would only apply to illegal immigrants who can prove they are spouses or relatives of U.S. citizens, legal residents or employees sponsored by employers before Aug. 14.

Families are being separated because the INS can't get its work done fast enough, Armey said.

"It is not right to let families be victimized by, if you will pardon the expression, bureaucratic indifference or incompetence," Armey said. "That is not right and we don't believe that is the way it should be."

Democrats want a longer time period, but House Democratic Leader Dick Gephardt of Missouri said they would support the bill anyway because "at least it's movement."

Republicans are "giving away as little as they can," said Gephardt, who said he would push later in the year for another bill that would extend the time allowed. "Their hearts are not really in this."

The Democrat-controlled Senate last year passed a bill that would extend the deadline for a year.

The Associated Press contributed to this report.