Barack Obama sought to stem the growing controversy over US surveillance program amid signs that a succession of revelations about federal spying on telephone and internet data is causing alarm in some sections of the Democratic party.

At the end of the first day of the his summit with the Chinese premier Xi Jinping in California, the president described disclosures about the National Security Agency's access to telephone and internet data as "a very limited issue".

However in comments that appeared more emollient than his remarks earlier in the day, when he criticised "leaks" and "hype" in the media, Obama tried to deflect criticism, saying internet privacy posed "broad implications for our society". He said privacy concerns also related to private corporations, which he said collect more data than the federal government.

Meanwhile America's tech giants bristled at the suggestions they had allowed the government direct access to their systems, as suggested by a top secret document prepared by the National Security Agency and published by the Guardian and the Washington Post.

With their credibility about privacy issues in sharp focus, technology companies said to be involved in the program, known as Prism, issued remarkably similar statements. They said they did not allow the government "direct access" to their systems, denied knowledge of the Prism program, and called for greater transparency.

Mark Zuckerberg, the Facebook founder and CEO, said: "Facebook is not and has never been part of any program to give the US or any other government direct access to our servers." Google and Facebook insisted that they only turned over data when they received a court order, and frequently challenged them.

But the New York Times reported on Saturday that major tech firms, including Google, Facebook and Microsoft, had co-operated with the NSA "at least a bit".

It said that Facebook and Google – and possibly other companies – discussed with security officials the construction of secure portals, in some cases on the company's servers, the article said. "Through these online rooms, the government would request data, companies would deposit it and the government would retrieve it," the Times reported. Twitter is said to have declined to participate.

At the Sunnylands resort in California, Obama disputed the suggestion that recent disclosures had undermined his talks with premier Xi, saying US concerns over hacking alleged to be emanating from China, which the administration hoped to address at the summit, were distinct from the controversy surrounding NSA surveillance programs.

"I think it's important … to distinguish between the deep concerns we have as a government around theft of intellectual property or hacking into systems that might disrupt those systems – whether it's our financial systems, our critical infrastructure and so forth versus some of the issues that have been raised around NSA programs," he said.

The president did not address the Guardian's latest disclosure of a top-secret presidential order directing senior national security and intelligence officials to draw up a list of potential overseas targets for US cyber-attacks.

The 18-page Presidential Policy Directive 20, issued in October last year but never published, states that what it calls Offensive Cyber Effects Operations (OCEO) "can offer unique and unconventional capabilities to advance US national objectives around the world with little or no warning to the adversary or target and with potential effects ranging from subtle to severely damaging".

Earlier on Friday evening, two Democratic senators, who are privy to top-secret briefings about NSA programs as part of their work on the Senate Intelligence Committee, released a statement strongly criticising comments made by senior administration officials and calling for more information to be declassified.

"After years of review, we believe statements that this very broad Patriot Act collection has been 'a critical tool in protecting the nation' do not appear to hold up under close scrutiny," senators Mark Udell and Ron Wyden said. "We remain unconvinced that the secret Patriot Act collection has actually provided any uniquely valuable intelligence."

For at least two years the pair have warned about secret government interpretations of the Patriot Act, but have been restricted in what they can say because their concerns stemmed from classified briefings that could not be publicly disclosed.

Ron Wyden joined other Democrats in criticising the NSA surveillance programs this week. Photograph: Jacquelyn Martin/AP

Taking issue with remarks made by Clapper and Obama, the senators said: "We disagree with the statement that the broad Patriot Act collection strikes the 'right balance' between protecting American security and protecting Americans' privacy," they said. "In our view it does not."

A third Democratic senator, Joe Manchin, said he was uncomfortable with the broad scope of NSA surveillance and indicated the attorney general, Eric Holder, should consider resigning.

Manchin told Bloomberg Television he was "bothered" by the breadth of NSA surveillance activities. "It should be stopped as far as the broad base that they're doing. If there's a profile and targeting that goes on, then fine," he said.

"I'm wanting to do everything I can to fight the war on terror," Manchin said. "There will not be another day in my life, my children or grandchildren's life they won't have to be vigilant against terrorists wanting to do us harm. But do you give up everything as an American?"

Until now, the response on Capitol Hill to the surveillance disclosures has been relatively muted, although some libertarians, such as Republican senator Rand Paul, who described the collection of telephone records as an "all-out assault on the constitution", have fiercely criticised the administration.

Even before the latest revelations, top Democrats had been expressing concern. After the Guardian reported a sweeping secret court against a subsidiary of Verizon, it emerged that the US government had been trawling vast amounts of phone data for at least seven years.

In a joint statement, prominent Democrats on the House judiciary committee, said in a statement reported by Politico: "We believe this type of program is far too broad and is inconsistent with our nation's founding principles." The statement was signed by the ranking Democrat, represenative John Conyers, among others.

Obama and senior administration officials insisted that Congress had been briefed repeatedly on the program. But the senators insisted that did not mean they agreed with it. "We strongly disagree with those who would assert that because this type of program appears to be long standing and members of Congress may have been briefed, that it is acceptable to us or the Congress," the statement said.