The measure has provoked a storm of protests, with civil libertarians claiming such laws could allow too much government snooping and conservatives say they would create new bureaucracy.
The lawmakers claim to be listening to those concerns, but explained that the issue has become more pressing recently with revelations about new cyber threats.
Greg Nojeim of the Center for Democracy and Technology said the changes failed to address one key concern — that information could be accessed by the NSA. The lawmakers said they would insert a more narrow definition of national security in the bill.
Lawmakers are expected to meet Wednesday to vote on the issue, which passed the House last year but died in the Senate.