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"I feel very proud of the role of the service and what it stands for and everything that we've done... Especially as it's had such a spotlight on it through (Trump's) usage and the election," Dorsey said on Tuesday.
"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," he said at a technology conference held in San Francisco, reported Xinhua news agency.
Trump, with nearly 17 million twitter followers, writes mostly about his feelings on domestic and international issues, while only five per cent of the total 34,000 tweets are retweets or quoted tweets.
The President-elect has written some 150 tweets in one month since the election after Trump said he would be "very restrained" about tweeting.
According to Dorsey, the US President-elect using Twitter as a direct line of communication "allows everyone to see what's on his mind in the moment", which is an "interesting and fascinating" phenomenon.