The top leaders from world’s biggest technology companies called on the US to "move aggressively" to reform the National Security Agency’s controversial surveillance operations after discussions with President Obama on Tuesday, resisting attempts by the White House to portray the encounter as covering a range of broader priorities.

Executives from 15 companies, including Google, Apple, Yahoo and Twitter, used a face-to-face meeting with Obama and vice-president Joe Biden to express their concern that the NSA’s wide-ranging surveillance activities had undermined the trust of their users.

The meeting came a day after a federal judge ruled that the NSA’s bulk collection of Americans’ phone records was “almost Orwellian” in scope and probably a violation of the US constitution. Some of the tech companies represented at the White House have already expressed deep concern at the wide-ranging nature of NSA surveillance, and the way it apparently draws information from their systems without their knowledge.

There was a clear division in how the White House event was characterised. In statements before and after, the administration was determined to point out that other issues were on the agenda, including the troubled federal healthcare website.

By contrast the tech companies made no mention of the healthcare website discussions. "We appreciated the opportunity to share directly with the president our principles on government surveillance that we released last week and we urge him to move aggressively on reform," they said in a joint statement issued after leaving the White House.

Two executives briefed on the discussions told the Guardian that the White House event took the form of a series of meetings that lasted two hours and 45 minutes. The healthcare website issues were discussed for only 45 minutes at most, and neither the president nor Biden were present for that part of the talks.

Discussions about the healthcare website and government IT issues were mostly restricted to a pre-meeting with Obama's chief of staff, Denis McDonough, and other advisors. It was only after that discussion was concluded that Obama and Biden arrived, at 10.45am, for the main scheduled discussion, which focused almost exclusively on surveillance issues.

Apart from a brief announcement by Obama about the appointment of a Microsoft executive to lead improvements to the healthcare website, the "the main topic of discussion" was NSA surveillance reform, according to one executive.

Specific topics that were raised included Prism, an NSA program that collects and mines internet communications, bulk collection of telephone records and reform of the secret Fisa courts. They also discussed the Electronic Communications Privacy Act, a 27-year-old law that allows emails and digital communications older than six months to be seized without a warrant.

Among those meeting Obama at the White House were Tim Cook, the CEO of Apple, Marissa Mayer, the CEO of Yahoo, and Eric Schmidt, Google’s executive chairman. Senior representatives from Comcast, Facebook, Microsoft, Twitter and Netflix were also there. So too was Randall Stephenson, the chairman and CEO of AT&T, one of the telecom providers routinely required to provide the NSA with metadata about its US customers.

The White House issued a statement saying the group had discussed “a number of issues of shared importance to the federal government and the tech sector, including the progress being made to improve performance and capacity issues with heathcare.gov”. It confirmed that Kurt DelBene, formerly vice-president of the Microsoft Office Division, would succeed Jeff Zients as senior advisor to health secretary Kathleen Sebelius as she tried to salvage the troubled website.

The White House did acknowledge that the NSA scandal had been discussed. “Finally, the group discussed the national security and economic impacts of unauthorized intelligence disclosures. This was an opportunity for the president to hear from CEOs directly as we near completion of our review of signals intelligence programs, building on the feedback we’ve received from the private sector in recent weeks and months,” it said.

“The president made clear his belief in an open, free, and innovative internet and listened to the group’s concerns and recommendations, and made clear that we will consider their input as well as the input of other outside stakeholders as we finalize our review of signals intelligence programs.”

Ahead of the meeting tech executives, who have clashed in private and public with the White House since the NSA revelations, called the other issues “peripheral”. An executive at one company represented at the White House on Tuesday, who declined to be named in order to discuss his company’s strategy, said: “There’s only one subject that people really want to discuss right now.”

Mike McGeary, founder of tech lobby group Engine, said tech executives were still feeling the aftershocks of the NSA revelations. “There is growing concern, especially among smaller companies, that they are at a competitive disadvantage because of these revelations.” He said US firms looking at international business were suffering from “perceived lack of security”.

“There were a lot of very concerned executives at the meeting today. They don’t really see problems with the Affordable Care Act as their primary focus,” said McGeary, whose membership includes Google, Mozilla and Yelp as well as a large number of Silicon Valley startups.

The Obama administration is now dealing with pressure on several fronts relating to the NSA. Monday’s court ruling sets up a legal chain of events that will almost certainly end up in the US supreme court. Judge Richard Leon’s ruling, which will now be subject to an appeal, concluded that the agency’s mass collection of phone records probably violates the fourth amendment, which prohibits unreasonable searches and seizures. Leon said James Madison, who played a key role in drafting the US constitution, would be “aghast” at the scope of the agency’s collection of Americans' communications data, were he alive today.

The president and his advisers were already considering the recommendations of an NSA review panel set up in the wake of Snowden’s revelations. They are also considering the future leadership of the agency, whose director and deputy director are stepping down.

The reverberations of Leon's ruling also echoed in Congress. Dianne Feinstein, the NSA's chief Senate supporter, again defended the program and disagreed with Leon, but stopped short of saying bulk phone records collection was essential to stop terrorism. In an interview with MSNBC on Tuesday, Feinstein, a California Democrat who chairs the Senate intelligence committee, urged the supreme court to determine its constitutionality. “I’m not saying it’s indispensable,” Feinstein said. “But I’m saying it is important, and it is a major tool in ferreting out a potential terrorist attack.”

In response to the Leon ruling, Feinstein said that other judges have blessed the constitutionality of the domestic call data program, and urged the highest court in the US to settle the issue. “Only the supreme court can resolve the question on the constitutionality of the NSA’s program,” Feinstein said a statement released after the interview.