Bossert said he expects more people will be affected when they log into their work computers today. FedEx was hit, but the situation is so far under control in the U.S.
Worldwide, the so-called WannaCry attack, which emerged Friday, has affected hundreds of thousands of computers by exploiting vulnerabilities in software.
"[The attack] is an urgent call for collective action" to guard against future cyberattacks, he said.
When a person logs into a computer that has been hacked, the screen is locked, and a link appears, urging the user to pay a ransom of $300 or more to have his or her data restored.
"We haven't ruled out that this is a state attack," he said.
He added that the U.S. government does not recommend paying the ransom and warned that making a payment to the hackers doesn't guarantee that access to computer files will be restored.
In a briefing today, Bossert said less than $70,000 has been paid in response to the cyberattacks.
ABC News Courtney Connley contributed to this report.