Airport security was heavily criticised after 11 September
The measures, backed by President George W Bush, will set stricter standards for private security firms, but will not make baggage screeners government employees - as the Senate had wanted.
And in another move designed to strengthen US laws, President Bush has proposed making it a crime to buy, build or acquire biological weapons for terrorist attacks.
There has been broad criticism of lax airport security in the US, following the hijackers which enabled the attacks on the World Trade Center and the Pentagon.
Under the planned airport security law, the government will be in charge of training screeners, air marshals will fly on commercial flights and cockpit doors will be secure.
Now the House and Senate versions of the legislation will go to a committee stage for further discussion.
But some congressmen fear that vital security moves could be delayed.
"My greatest fear is that if it goes to a conference, it never comes out," said House Democratic leader Richard Gephardt.
California threat
On Thursday California Governor Gray Davis said he had received "credible" information that major bridges in the state - including the Golden Gate Bridge - could be targeted for attack.
Security was tightened at all four bridges, but Mr Gray's spokesman later said that the governor had only learned of "a possible threat to bridges in the western states".
Mr Davis mentioned the Golden Gate and Bay Bridges in San Francisco, the Vincent Thomas Bridge in Los Angeles and the Coronado Bridge in San Diego as being under threat.
But his spokesman, Steve Maviglio, said these had merely been examples of the sorts of bridges to which the threat could apply.
There are no plans to close the bridges.
A spokeswoman at the US Justice Department in Washington said the warning was one of many that FBI officials had issued around the country since 11 September, adding that there was no specific reason to give this one more weight.
Clampdown
As well as proposing to make trading in biological weapons for terrorist attacks a crime, President Bush also recommended that the United Nations should devise a means to investigate suspected biological warfare attacks.
The move - a proposed strengthening of the 1972 UN Biological and Toxic Weapons Convention - appears to be a reversal of policy for the White House, which was reluctant to back international treaties before 11 September.
If confirmed, the finding would make the FDA the latest branch of the US Government to be affected by anthrax.
The disease has also been discovered at a mail processing facility in Kansas City, Missouri - the first incidence in the Midwest.
Postal facilities in New Jersey, New York and Washington have already been hit by the bacteria and traces of anthrax in several federal buildings have interrupted the work of America's executive, legislative and judicial powers: