In a report to be published on Monday, and provided in advance to The New York Times, Kaspersky Lab says that the scope of this attack on more than 100 banks and other financial institutions in 30 nations could make it one of the largest bank thefts ever — and one conducted without the usual signs of robbery.

The Moscow-based firm says that because of nondisclosure agreements with the banks that were hit, it cannot name them. Officials at the White House and the F.B.I. have been briefed on the findings, but say that it will take time to confirm them and assess the losses.

Kaspersky Lab says it has seen evidence of $300 million in theft through clients, and believes the total could be triple that. But that projection is impossible to verify because the thefts were limited to $10 million a transaction, though some banks were hit several times. In many cases the hauls were more modest, presumably to avoid setting off alarms.

The majority of the targets were in Russia, but many were in Japan, the United States and Europe.

No bank has come forward acknowledging the theft, a common problem that President Obama alluded to on Friday when he attended the first White House summit meeting on cybersecurity and consumer protection at Stanford University. He urged passage of a law that would require public disclosure of any breach that compromised personal or financial information.

But the industry consortium that alerts banks to malicious activity, the Financial Services Information Sharing and Analysis Center, said in a statement that “our members are aware of this activity. We have disseminated intelligence on this attack to the members,” and that “some briefings were also provided by law enforcement entities.”