The outages left another bruise on a service that earned a reputation for unreliability in its early days.
The San Francisco-based company blamed the disruption on a "cascading bug" in one of its infrastructure components.
"One of the characteristics of such a bug is that it can have a significant impact on all users, worldwide, which was the case today," Mazen Rawashdeh, a Twitter vice president of engineering, wrote in a blog post after normal service resumed.
"This wasn't due to a hack or our new office or Euro 2012 or GIF avatars, as some have speculated today."
"We are currently conducting a comprehensive review to ensure that we can avoid this chain of events in the future," he added.
Twitter's statements came amid speculation that hackers contributed to the disruption.
UgNazi - an emerging hacker outfit that recently gained publicity for breaking into Cloudflare chief executive Matthew Prince's personal Google email account - claimed credit for the service disruption in an email to Reuters, saying it launched a distributed denial-of-service (DDoS) attack against Twitter because of the company's support for the Cyber Intelligence Sharing and Protection Act.
One security professional said the group probably used a DDoS-for-hire site to launch an attack against Twitter on Thursday, but played down the likelihood the group was responsible for bringing down the social media network.
"It was mere coincidence," the security professional said. "The backend of Twitter is having issues, which is unrelated to the very small attack."
North American traffic levels for Twitter.com plummeted on two occasions between 8.30 a.m. PDT (1530 GMT) and 11.00 a.m. PDT (1800 GMT), according to data provided by network analytics company Sandvine.
The first outage lasted between 8.30 a.m. (1530 GMT) and 10.00 a.m. (1700 GMT), data showed.
Twitter acknowledged the disruption in a mid-morning blog post that was continually revised as the service resumed, only to fail for a second time before 11.00 a.m.
As the service resumed on Thursday, its most dedicated users quickly hopped back on to crack jokes, express relief and complain that during the outage they had nowhere to complain about the interruption.
Founded in 2006, Twitter was plagued in its early days by frequent outages as it struggled to handle the ever-rising volume of tweets, leaving frustrated users with its famous "fail whale" error screen.
In recent years, Twitter, under pressure to demonstrate financial viability, has devoted considerable resources toward improving reliability in a move to project itself as a mature, polished brand.
CEO Dick Costolo said this month that Twitter now has 140 million active monthly users who send 400 million tweets daily.
The company conceded on Thursday it had failed users who rely on it to connect with "heroes, causes, political movements."
"It's imperative that we remain available around the world," said Rawashdeh, "and today we stumbled."