The administration of U.S. President Barack Obama urged the Senate to pass the USA Freedom Act, which would curb the bulk collection of telephone records by the National Security Agency in the wake of widespread concerns about potential violations of privacy.

The administration has asked the Senate to pass the legislation and for the House of Representatives, which earlier passed a weakened version of the bill, to act quickly so that Obama can sign the legislation into law this year, according to a statement Monday from the executive office of the president. The bill has to pass both in the Senate and the House before it can become law.

A procedural vote in the Senate on the legislation, which has got the backing of civil rights activists and other groups, could come on Tuesday, with a final vote on the bill in the days following.

“The bill strengthens the FISA’s privacy and civil liberties protections, while preserving essential authorities that our intelligence and law enforcement professionals need,” according to the statement, which noted that the administration “strongly supports” Senate passage of the legislation. If the bill is not passed, critical national security authorizations that are reformed in the legislation could expire next summer, it added.

The administration is, however, hopeful that the legislation will resolve concerns from intelligence officials about a provision in the bill that allows an independent privacy advocate to argue before the FISA Court in support of individual privacy and civil liberties. The Foreign Intelligence Surveillance Act, better known as FISA, governs NSA surveillance.

Former NSA contractor Edward Snowden triggered strong privacy concerns in the U.S. and abroad after his disclosures last year that the government was collecting telephone metadata of Americans in bulk from Verizon and also intercepting Internet communications, placing technology companies in an embarrassing position with their users.

A number of countries are now demanding that cloud companies store data locally to avoid access to the information by U.S. law enforcement.

The Senate bill requires the NSA to use specific selection terms to limit its targets in the telephone records collection, and requires the government to issue reports on the number of people targeted in surveillance programs.

The bill introduced by Senator Patrick Leahy, a Democrat from Vermont, is a version of the bill passed in the House, which was criticized by privacy advocates for watering down key privacy provisions, including in the criteria for search terms to collect phone records.

Some critics of the bill, however, argue that the USA Freedom Act does not address surveillance and data collections under other provisions such as Section 702 of the amended FISA Act, which covers surveillance of non-U.S. persons located outside the U.S.

A group of technology companies have also released an open letter to the Senate, urging that it pass the bill. The letter from the Reform Government Surveillance coalition is backed by Facebook, Apple, Twitter, Google, Microsoft and other companies.

The technology companies, however, described the legislation as only a first step in reform around the world. The group is demanding reforms in areas such as preventing government access to data without proper legal process, and is seeking assurances that providers are not required to locate infrastructure within a country’s border.