It's "complicated," said Dorsey, giving a carefully-worded responses when asked Tuesday about the president-elect's tweets at Recode's Code Commerce conference in San Francisco.
"I feel very proud of the role of the service and what it stands for," Dorsey continued. "Especially as it's had such a spotlight on it through (Trump's) usage and the election, but the elections have always been big on Twitter."
Trump, who has estimated having roughly 30 million followers on social media, including nearly 17 million on Twitter, has praised social media for effectively combatting traditional media outlets. Social media analysis groups have said Trump routinely generated more comments than his opponents during the grueling election.
Trump's regular, and sometimes controversial, use of Twitter left many people scratching their heads, including Dorsey.
"The complicated part...is just what does this mean to have a direct line to how he's thinking in real-time and to see that," Dorsey said Tuesday. "I'm not sure."
He also admitted that he's fascinated -- like most of us -- by Trump's mastery of tweets.
"Having the president-elect on our service, using it as a direct line of communication, allows everyone to see what's on his mind in the moment," Dorsey said. "I think that's interesting. I think it's fascinating."
Dorsey said Twitter plays a big part in distributing news and opinions and has a responsibility "to make sure that people are seeing what they need to see." He seemed unclear how Trump's continued use of Twitter might affect social media in the future.
"We're definitely entering a new world where everything is on the surface and we can all see it in real time and we can all have conversations about it," he said. "Where does that go, I'm not really sure? But it's definitely been fascinating to learn from."