Pressure is building within the US Senate for an overhaul of the secret court that is supposed to act as a check on the National Security Agency's executive power, with one prominent senator describing the judicial panel as "anachronistic" and outdated.

Ron Wyden, a Democratic senator for Oregon, said discussions were under way about how to reform the Foreign Intelligence Surveillance court, the body entrusted with providing oversight on the NSA and its metadata-collecting activities. He told C-Span's Newsmaker programme on Sunday that the court, which was set up in 1978 under the Foreign Intelligence Surveillance Act (Fisa), was ill-equipped to deal with the massive digital dragnet of millions of Americans' phone records developed by the NSA in recent years.

"In many particulars, the Fisa court is anachronistic – they are using processes that simply don't fit the times," Wyden said.

The Oregon senator is at the forefront of a growing chorus of political voices criticising the Fisa court for being biased towards the executive branch to the exclusion of all other positions. "It is the most one-sided legal process in the US, I don't know of any other legal system or court that doesn't highlight anything except one point of view – the executive point of view."

Wyden added: "When that point of view also dominates the thinking of justices, you've got a fairly combustible situation on your hands."

The court's secretive deliberations were first revealed in June by the Guardian which published its order approving the collection of phone Verizon phone records. The order was among a raft of top secret documents leaked to the Guardian and Washington Post by the former NSA contractor Edward Snowden.

Since the Guardian's disclosure, attention has grown on the composition and practices of the Fisa court. The New York Times has shown how the court has secretly expanded its operations until it now holds the status almost of a parallel supreme court.

The Times has also analysed the make-up of the court and discovered an alarming bias within the ranks of its judges in favour of government. More than a third of the justices appointed to the court since its inception have had executive branch experience.

On Sunday, the prominent Democratic senator for Illinois, Dick Durbin, added his voice to the mounting criticism of the Fisa court, telling ABC's This Week: "There should be a real court proceeding. In this case, it's fixed in a way, it's loaded. There's only one case coming before the Fisa, the government's case. Let's have an advocate for someone standing up for civil liberties to speak up about the privacy of Americans."

The outcry from Durbin and Wyden chimes with other moves within the US Senate to reform the way the court is constructed. Adam Schiff, a Democratic member of the House intelligence committee, has tabled legislation that would transfer the power to nominate judges to the court from the chief justice of the US supreme court, John Roberts, as is the current arrangement, to President Obama subject to senate approval.

The groundswell for reform received a boost from last week's narrow vote in the House of Representatives over a move to cut off federal funding for the NSA's metadata-gathering activities. The proposal to knock back the agency's collection of the phone records of millions of Americans was defeated by 217 to 205 votes, but more than half of the Democratic caucus in the House as well as 94 Republicans voted in favour of reform.

Wyden said that the vote has acted as a stimulus to discussions about NSA reform. "You are going to see a very strong and bipartisan effort in the Senate to pick up on the work of the House."

This week, the congressional debate about how to deal with anxieties over the NSA's data collection methods is certain to flair up again. On Wednesday, two congressional hearings will be held in which both sides of the argument are likely to be forcefully presented.

Those opposing positions were reflected in Sunday's political TV talk shows. Mike Rogers, chair of the Republican-led House intelligence committee, told NBC's Meet the Press that the NSA did not spy on Americans and that no names or addresses were included in its databases of phone records. "In this programme: zero privacy violations, 54 terrorist plots foiled – that's a pretty good record," he said.

Peter King, a congressman for New York, slammed fellow Republicans who had voted to cut off funding for the NSA sweep of phone records. "I thought it was absolutely disgraceful that so many Republicans voted to defund the NSA programme, which has done so much to protect our country," he told CNN.

On the other side of the argument, Mark Udall, Democratic senator from Colorado, told Face the Nation on CBS that he regarded the dragnet of phone records of millions of Americans as something that "comes close to being unconstitutional".