John McCain, the Republican senator and former presidential candidate, has called for a congressional investigation into America’s “broken” National Security Agency, ahead of week in which the White House will announce its own reforms.

President Barack Obama will reveal a number of changes to the way the NSA and associated secret courts operate on Friday, concluding months of debate within the administration about the appropriate response to disclosures made by the whistleblower Edward Snowden.

The Obama administration is desperate to draw a line under the controversy that has engulfed the NSA over the last six months. The president’s proposals are partly based on the findings of a major review, commissioned in the aftermath of the Snowden disclosures, which recommended, among other things, that the agency should no longer collect and store domestic phone records.

McCain told CNN on Sunday that Congress was probably going to need to pass legislation to implement Obama’s recommendations, and was obliged to run its own investigation into the wider controversy over US surveillance.

“Is there anybody believes that this system is not broken in many respects? I think not,” he said.

“There has been overreach, it seems to me,” he added. “Sometimes these agencies have done things just because they can. I think we need a select committee in Congress to go over this whole scenario, because it does overlap many committees.”

Select committees are ad-hoc panels, often instituted to look into major scandals. They can have investigative powers and the authority to summons witnesses.

This is not the first time McCain has called for a congressional investigation into the NSA, pointing out, as civil liberty advocates have done, that existing intelligence committees have failed their mandate to hold agencies to account.

The Electronic Frontier Foundation, a digital rights group, has called from a congressional investigation modelled on the Church Committee, which in the 1970s looked into domestic surveillance. There appears to be little appetite in Washington for such a wide-ranging inquiry, but the White House is keen to maintain the support of prominent lawmakers.

Obama and his national security officials have in recent days met legislators, technology firms and privacy advocates to prepare the ground for Friday’s announcement. “The debate is clearly fluid,” Democratic senator Ron Wyden told the Guardian after meeting the president on Thursday. “My sense is the president, and the administration, is wrestling with these issues.”

The intelligence community has been engaged in its own last-minute lobbying, seeking to persuade the White House to hold back from implementing any substantial changes to the way it conducts surveillance, such as increasing the legal threshold required to search or obtain data pertaining to Americans who are not suspects.

The public debate has largely ignored the issue of surveillance on foreigners, which even Congress’s critics appear happy to leave largely unchanged. An exception, perhaps surprisingly, has been Obama, who highlighted concerns raised by his review panel about the lack of regulations relating to foreign surveillance.

“In some ways, what has been more challenging is the fact that we do have a lot of laws and checks and balances and safeguards and audits when it comes to making sure that the NSA and other intelligence agencies are not spying on Americans,” he said in December.

“We’ve had less legal constraint in terms of what we’re doing internationally … and the values that we’ve got as Americans are ones that we have to be willing to apply beyond our borders I think perhaps more systematically than we’ve done in the past.”