The National September 11 Memorial & Museum says it has raised more than $700 million so far.
It outlined its funding in a statement seeking federal funding authorization.
The statement says the authorization would "help advance core national priorities at a site of international importance."
A Senate subcommittee was meeting on the proposed legislation in Washington on Wednesday.
Memorial officials say nearly $500 million of the funds raised so far have come from non-federal sources. The proposed legislation would provide about one-third of the group's operating budget.
Organizers say most of the funds have been used for construction and planning the museum. It's slated to open next year.