Congressional critics of the National Security Agency said they welcomed President Obama's intention to work closely with lawmakers on oversight of surveillance programs, but said they would continue to press for additional reforms.

Obama on Friday announced a number of changes to the agency’s phone and internet surveillance, including requiring court approval before the NSA can access phone metadata and moving away from the government storing that information.

Sen. Rand Paul, R-Ky., one of the GOP's top NSA critics, said Obama's proposed changes were a good first step but did not satisfy his concerns.

“President Obama's announced solution to the NSA spying controversy is the same unconstitutional program with a new configuration,” Paul said.

“I intend to continue the fight to restore Americans rights through my Fourth Amendment Restoration Act and my legal challenge against the NSA,” he added. ”The American people should not expect the fox to guard the hen house.”

Sens. Ron Wyden, Mark Udall and Martin Heinrich, three Democrats who have aggressively pushed for major changes to the nation's spying programs, in a joint statement called Obama's announcement a “major milestone” that will “go a long way in restoring Americans' constitutional rights and rebuilding the public's trust.”

But they also called Obama's announcement “a vindication” and vowed to continue their fight for a broader overhaul in the coming weeks and months.

The president’s steps were announced in a speech at the Justice Department following Obama’s review of 46 recommendations from an outside panel.

Some on Capitol Hill said Obama’s call to remove phone metadata collection from the government would open up an entirely new debate over who should store the data and under what conditions the intelligence community could access it.

“Significant policy questions remain, including who should house this data,” said Sen. Dean Heller, R-Nev., who has co-authored several bills aimed at reining in the NSA.

“I have concerns that requiring private companies to shoulder the burden for the NSA could simply shift privacy intrusions from the federal government to private companies,” he added.

Wyden, Udall and Heinrich said they will work to close the “back-door searches” loophole, a gap in the law that allows the NSA to conduct warrantless searches for phone calls and emails of law-abiding Americans, and to ensure that intelligence activities do not “recklessly undermine confidence” in tech companies and their products.

“Today’s announcement does not include all the reforms we have sought… the fight to protect liberty and increase security is far from over,” they said.

But others in Obama’s party said the president had taken a balanced approach to weighing the nation’s security interests and the privacy concerns of the public.

“I give the president credit for offering a robust and historic blueprint for reform,” said Sen. Richard Blumenthal, D-Conn.

Blumenthal said he was encouraged that Obama is going to set up a privacy advocate on the Foreign Intelligence Surveillance Court, a key change he has pushed for months.

In his address, Obama also briefly mentioned Edward Snowden, the leaker who disclosed the nation's secret surveillance programs and fled to Russia, where he received amnesty.

Obama said he would not “dwell on Mr. Snowden’s actions or motivations.” But Obama warned that if individuals who disagreed with government policies “can take it in their own hands to publicly disclose classified information, then we will never be able to keep our people safe or conduct foreign policy.”

Some liberal groups said Obama should allow Snowden, who is facing espionage and theft charges, to return to the U.S., pointing out that without his leaks, the nation would not have had a debate over the NSA’s practices.

“[Snowden] is a hero and whistleblower, and deserves clemency,” Karissa Gerhke, an organizer for the Progressive Change Campaign Committee, said in a statement.

White House officials and leaders of the intelligence committees in Congress say Snowden violated U.S. law and should return to face trial.

This story was published at 1:06 p.m. and has been updated.