The former director of the US National Security Agency has indicated that surveillance programs have "expanded" under Barack Obama's time in office and said the spy agency has more powers now than when he was in command.

Michael Hayden, who served most of his tenure as NSA director under George W Bush, said there was "incredible continuity" between the two presidents.

Hayden's comments came as the debate around the extent of government surveillance in the US and the UK intensified on Sunday. In Washington, some US senators demanded more transparency from the Obama administration. Libertarian Republican Rand Paul said he wanted to mount a supreme court challenge.

The British foreign secretary, William Hague, announced he would make a statement to parliament on Monday after the Guardian revealed that UK intelligence agencies used the US Prism system to generate intelligence reports.

Hague said it was "fanciful" and "nonsense" to suggest that the British monitoring service, GCHQ, would work with an agency in another country to circumvent restrictions on surveillance in the UK.

The issue dominated the Sunday talk shows on both sides of the Atlantic. On CNN, senator Mark Udall, one of the prominent Senate critics of US government surveillance, called for amendments to the Patriot Act, the controversial law brought in after the 9/11 attacks, to rein in the NSA's powers. "I'm calling for reopening the Patriot Act," Udall said. "The fact that every call I make to my friends or family is noted, the length, the date, that concerns me."

Udall, who has been privy to classified briefings about NSA data collection programs, said it was unclear to him that the surveillance initiatives had disrupted terrorist plots, as the administration has claimed.

He called on Obama's administration to make more information about the programs public. "The ultimate check, the ultimate balance is the American public understanding to what extent their calls are being collected, if only in the sense of metadata," he said. "Let's not have this law interpreted secretly, as it has been for the last number of years."

Wyden

Paul

Udall's Democratic colleague Ron Wyden, who has had access to the same confidential briefings, and also spoken out over the surveillance programs, told the Guardian he believed the White House needed to address whether previous statements "are actually true".

"Since government officials have repeatedly told the public and Congress that Patriot Act authorities are simply analogous to a grand jury subpoena, and that intelligence agencies do not collect information or dossiers on millions or hundreds of millions of Americans, I think the executive branch has an obligation to explain whether or not these statements are actually true," Wyden said.

On Fox News, Paul, the Kentucky senator, said the disclosures were a wake-up call. "I'm going to be seeing if I can challenge this at the supreme court level," he said. "I'm going to be asking all the internet providers and all of the phone companies: ask your customers to join me in a class action lawsuit. If we get 10 million Americans saying we don't want our phone records looked at, then maybe someone will wake up and something will change in Washington."

Speaking on CNN, Republican senator John McCain defended the government's surveillance efforts, although he said members of Congress needed to be briefed in more detail about NSA activities. "If this was September 12, 2001, we might not be having the argument we are having today," he said. "Yes, perhaps there's been some overreach."

The Senate intelligence committee chairwoman, Dianne Feinstein, a Democrat, also justified the surveillance programs, arguing they were subject to congressional and judicial oversight and have contributed to the arrest to two terror suspects: David Headley and Najibullah Zazi.

Defending the practices on ABC's This Week, Feinstein said she flew over the World Trade Center in New York on the way to the funeral of Senator Frank Lautenberg. "I thought of those bodies jumping out of the building, hitting the canopy."

Hayden, who ran the NSA between 1999 and 2005, where, after September 11, he presided over the creation of secret, warrantless surveillance that collected information on Americans' communication, said the efforts had worked. "We've had two very different presidents pretty much doing the same thing with regard to electronic surveillance. That seems to me to suggest that these things do work."

Asked on Fox News Sunday how Obama had dealt with NSA programs since coming to office, Hayden replied: "In terms of surveillance? Expanded [the programs] in volume, changed the legal grounding for them a little bit – put it more under congressional authorisation rather than the president's Article 2 powers – and added a bit more oversight. But in terms of what NSA is doing, there is incredible continuity between the two presidents."

He added: "We've gotten more of these records over time. With the amendment to the Fisa Act, in 2008, which Senator Obama finally voted for, NSA is actually empowered to do more things than I was empowered to do under President Bush's special authorisation."

Hayden was confirmed as CIA director in 2006. Obama, who was a senator at the time, voted against Hayden's appointment, in protest against the NSA's surveillance on Americans.

Defending the mass collection of phone data from telecom providers, revealed on Wednesday when the Guardian published a secret court order requiring Verizon to data from millions of customers, Hayden said the NSA only stores the data for use in future terrorist investigations.

He said that safeguards were in place, ensuring there was always a "probable cause" or "arguable reason" before the database is scrutinised for intelligence about individuals connected to suspects.

Mike Rogers, the Republican chairman of the House intelligence committee, condemned the leaks and said the media's sources should be investigated for potential criminal activity.

"Taking a very sensitive classified program that targets foreign person on foreign lands, and putting just enough out there to be dangerous, is dangerous to us, it's dangerous to our national security and it violates the oath of which that person [the whisteblower] took," he told ABC's George Stephanopoulos. "I absolutely think they should be prosecuted."

Speaking on the BBC, Hague said the UK has enjoyed an "exceptional intelligence sharing relationship" with the US since the second world war. But he said that information from the US which is sent to Britain is governed by UK law.

Hague, who said he authorises operations by GCHQ most days of the week, said: "The idea that in GCHQ people are sitting working out how to circumvent a UK law with another agency in another country is fanciful. It is nonsense."

He said GCHQ, MI5 and MI6 were overseen by the relevant secretary of state, by the interception commission and by parliament's intelligence and security committee.

"If you are a law-abiding citizen of this country going about your business and your personal life you have nothing to fear – nothing to fear about the British state or intelligence agencies listening to the contents of your phone calls or anything like that. Indeed you will never be aware of all the things those agencies are doing to stop your identity being stolen and to stop a terrorist blowing you up tomorrow."