RSA Security is offering to provide security monitoring or replace its well-known SecurID tokens—devices used by millions of corporate workers to securely log on to their computers—"for virtually every customer we have," the company's Chairman Art Coviello said in an interview.

In a letter to customers Monday, the EMC Corp. unit openly acknowledged for the first time that intruders had breached its security systems at defense contractor Lockheed Martin Corp. using data stolen from RSA.

SecurID...