WASHINGTON — Leaders of the nation’s biggest technology firms warned President Barack Obama during a lengthy meeting at the White House on Tuesday that National Security Agency spying programs are damaging their reputations and could harm the broader economy.

Cisco has said it is already seeing customers, especially those overseas, back away from U.S. branded technology after documents revealed the NSA enlisted tech firms and also secretly tapped into their data hubs around the world as the agency pursued terrorism suspects. Other companies, such as IBM, AT&T and Verizon, are facing angry shareholders, some of whom have filed lawsuits demanding that the companies disclose their participation in NSA intelligence programs.

Silicon Valley has been a critical driver of the economic recovery and has long represented the face of American ingenuity around the world. Many of these companies say they are still trying to assess the damage caused by documentation of their work with intelligence officials, as revealed by former NSA employee Edward Snowden.

But some shareholders say Silicon Valley has been slow to recognize the reputational crisis that is developing around the world for these companies.

“Verizon and AT&T are not managing this crisis effectively,” said Jonas Kron, director of shareholder advocacy at Trillium, an $1.3 billion investment fund. “Now is the time for these companies to demonstrate that they will protect user privacy, because it is in the interest of everyone – investors, citizens, our nation and the companies.”

The morning meeting at the White House, held in the Roosevelt Room, took on added import given a federal judge’s ruling Monday that the NSA’s program to conduct broad phone surveillance appears to be unconstitutional. That, along with the outcry from Silicon Valley and civil liberty advocates, some of whom belong to Obama’s own party, is increasing pressure on the administration to curb NSA surveillance efforts.

The gathering was scheduled for two hours but went well over the allotted time, with the majority of the discussion focused on the companies’ demands for government reforms of NSA spying programs, according to tech industry officials familiar with the talks who spoke on condition of anonymity to speak freely about the meeting.

Several of the executives came to the meeting particularly angered over a recent report in The Washington Post that revealed the NSA and its British counterpart, GCHQ, were secretly tapping into the data connections that link Google and Yahoo servers around the world, industry officials said.

Their message was to say: “What the hell are you doing? Are you really hacking into the infrastructure of American companies overseas? The same American companies that cooperate with your lawful orders and spend a lot of money to comply with them to facilitate your intelligence collection? Really?” said one industry official familiar with the companies views.

In the meeting, the executives reiterated a list of demands that had been sent to the White House in a letter last week calling on the administration to cease bulk data collection of emails, online address books and other personal information, to impose limits on how easily the NSA can obtain court orders for Internet data and to allow the companies to be more transparent about government intelligence requests.

Senior administration officials described the meeting with the 15 executives as “constructive, not at all contentious.”

“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,” the White House said in a statement.

News photos of the meeting showed AT&T chief executive Randall Stephenson smiling next to Obama and Yahoo chief executive Marissa Mayer also smiling, seated next to Vice President Joe Biden.

Also in attendance were the chief executives of Apple, Netflix, and Twitter, among others. Senior executives from Microsoft, Facebook, Google, Linked in, and Zynga also came.

“We appreciated the opportunity to share directly with the President our principles on government surveillance that we released last week and we urged him to move aggressively on reform,” the technology firms said in a joint statement after the meeting.

Many of these high-tech firms have played a key role in boosting Obama’s political fortunes. Tech companies pumped nearly $7.8 million into his campaign last cycle, more than double the tally for Republican challenger Mitt Romney, according to the non-partisan Center for Responsive Politics.

Some of the top officials meeting with the president Tuesday served as bundlers for his 2012 bid: Mayer, Yahoo’s chief, raised between $100,000 and $200,000, according to the Center for Responsive Politics, while Shervin Pishevar, co-founder of Sherpa Global, an technology investment fund, raised more than $500,000. Mark Pincus, Zynga’s chief product officer and chairman, gave $1 million to Priorities Action USA, the super PAC affiliated with Obama.

Still, some of these executives, as well as their shareholders, are growing worried about the bottom-line impact of the NSA intelligence programs.

In its earnings report last month, Cisco executives explained that disappointing sales in emerging markets were partly tied to the NSA leaks. It may have “caused a number of customers to pause and re-evaluate,” Cisco’s head of sales, Robert Lloyd, said at the time.

Last week, IBM’s shareholders sued the company in a New York federal court, saying the company harmed investors with its secret participation in NSA programs.

“IBM’s association with the NSA presented a material risk to the company’s sales and, in particular … sales in China that were of critical importance to investors,” the Louisiana Sherriff’s Pension and Relief Fund said in its lawsuit. “Despite that knowledge . . . IBM misrepresented to investors that it was a market leader in the Asia-Pacific region and that IBM expected solid improvement in the sales of its hardware division.”

Last month, shareholders of Verizon and AT&T also demanded the companies disclose their participation in NSA intelligence programs.

The $160.7 billion New York State Common Retirement Fund filed a resolution with AT&T’s board to make public its participation with government intelligence programs. Customers can too easily switch to another wireless carrier amid concerns AT&T is sharing telephone data and other information with the government, the pension fund argued.

“This is a significant policy issue for shareholders and we believe that AT&T must take meaningful steps toward disclosing how it safeguards customer privacy,” said New York State Comptroller Thomas DiNapoli.

The meeting at the White House was the second time top Silicon Valley and telecom leaders have convened with Obama after government contractor Edward Snowden began to release portions from a trove of top-secret documents detailing NSA spying programs.

Obama tried to keep the tenor friendly, even cracking jokes, the industry official said.

At one point, he asked Netflix chief executive Reed Hastings if he brought advanced copies of the second season of “House of Cards,” a satire-drama of Washington politics, according to a pool report of the meeting.

Hastings laughed and invited Obama to do a cameo appearance on the show. Obama said of the ruthless lead character, a Senator played by Kevin Spacy, “This guy’s getting a lot of stuff done.”

“I wish things were that ruthlessly efficient,” Obama said, to laughter from all the tech executives.