The bill also would make it easier for judges to deport immigrants seeking political asylum if they think they might be terrorists.
Many governors and state motor vehicle departments oppose the bill because it would be costly and would require them to become involved in enforcing immigration policies.
“Common sense says we should not allow suspected terrorists to be able to stay inside our borders if they could harm us,” said House Speaker Dennis Hastert.
Although rejected by Congress in December when it was part of a larger bill to reorganize the U.S. intelligence agencies, this new bill has now received support from the Bush administration.
To become law, the bill must still pass the Senate, which could prove difficult. Some Republican legislators have said they'd rather see it become part of a larger immigration bill.