Representatives of American Express confirmed that the company was under attack Thursday, but said that there was no evidence that customer data had been compromised. A representative of the Federal Bureau of Investigation did not respond to a request for comment on the American Express attack.

Spokesmen for JPMorgan Chase said they would not talk about the recent attack there, its origins or its consequences. JPMorgan has openly acknowledged previous denial of service attacks. But the size and severity of the most recent one apparently led it to reconsider.

The Obama administration has publicly urged companies to be more transparent about attacks, but often security experts and lawyers give the opposite advice.

The largest contingent of instigators of attacks in the private sector, government officials and researchers say, remains Chinese hackers intent on stealing corporate secrets.

The American and South Korean attacks underscore a growing fear that the two countries most worrisome to banks, oil producers and governments may be Iran and North Korea, not because of their skill but because of their brazenness. Neither country is considered a superstar in this area. The appeal of digital weapons is similar to that of nuclear capability: it is a way for an outgunned, outfinanced nation to even the playing field. “These countries are pursuing cyberweapons the same way they are pursuing nuclear weapons,” said James A. Lewis, a computer security expert at the Center for Strategic and International Studies in Washington. “It’s primitive; it’s not top of the line, but it’s good enough and they are committed to getting it.”

American officials are currently weighing their response options, but the issues involved are complex. At a meeting of banking executives, regulators and representatives from the departments of Homeland Security and Treasury last December, some pressed the United States to hit back at the hackers, while others argued that doing so would only lead to more aggressive attacks, according to two people who attended the meeting.

The difficulty of deterring such attacks was also the focus of a White House meeting this month with Mr. Obama and business leaders, including the chief executives Jamie Dimon of JPMorgan Chase; Brian T. Moynihan of Bank of America; Rex W. Tillerson of Exxon Mobil; Randall L. Stephenson of AT&T and others.