Twitter confirmed that the company's domain records were modified and that some users were unable to view images on the site. But the company said no user information was affected.
The Huffington Post confirmed the attack to The Wall Street Journal and said there was only a "minimal disruption of service."
The cyberattacks came as the United States and other nations consider military strikes against Assad's government over its suspected use of chemical weapons.
Eileen Murphy, a spokeswoman for The New York Times, said that "the outage was the result of an external attack on our domain name registrar."
But she said the company has no way of confirming whether the attack was carried out by the Syrian Electronic Army or a group pretending to be them.
Melbourne IT, the Times' domain name registrar, told The Los Angeles Times that the hackers gained access to the username and password of one of the company's sales partners.
The hackers were able to use that information to redirect nytimes.com traffic to their own servers. The information also enabled the attacks on Twitter and The Huffington Post.
The Syrian Electronic Army has previously claimed credit for other hacks of media companies, including sending a false message from The Associated Press's Twitter account earlier this year about an explosion at the White House. The message briefly caused stock prices to tumble.
But Marc Frons, the Times's chief information officer, explained in an interview with the newspaper that Tuesday's infiltration of the domain registrar was far more serious than the previous hacks.
“In terms of the sophistication of the attack, this is a big deal,” Frons said. “It’s sort of like breaking into the local savings and loan versus breaking into Fort Knox. A domain registrar should have extremely tight security because they are holding the security to hundreds if not thousands of Web sites.”