Due to defensive measures Twitter took against Thursday's denial-of-service attack, some Twitter clients cannot connect to the site, and many users are unable to tweet via SMS, the company announced Friday.
Twitter said it is working as quickly as possible to restore its service.
"The attacks have continued in their intensity and changed in their nature over the past 24 hours, and we're working this morning to restore access to applications built on the Twitter platform," Twitter co-founder Biz Stone said in a statement.
"Regarding insights into the attack, they appear to be geopolitical in motivation. However, we don't feel it's appropriate to engage in speculative discussion about these motivations," Stone said. "The open exchange of information can have a positive impact globally and our job is to keep Twitter services running reliably to the best of our ability."
Hackers on Thursday shut down the fast-growing messaging service Twitter for hours, while Facebook experienced intermittent access problems.
Twitter said it suffered a denial-of-service attack, in which hackers command scores of computers toward a single site at the same time, preventing legitimate traffic from getting through.
The attacks may have been related to the ongoing political conflict between Russia and Georgia.
They started with hackers using a botnet to send a flurry of spam e-mail messages that contained links to pages on Twitter, Facebook and other sites written by a single pro-Abkhazia activist, according to Bill Woodcock, research director of the San Francisco-based Packet Clearing House, a nonprofit that tracks Internet traffic.
When people clicked on the links, they were taken to the activist's legitimate Web pages, but the process of loading the pages at such volumes overwhelmed some servers and disrupted service, Woodcock said.
According to comScore, Twitter had 20.1 million unique visitors in the United States in June, some 34 times the 593,000 a year earlier.
The Twitter outage began at about 9 a.m. EDT and lasted a few hours.