Dorsey, in addition to stepping in for outgoing Twitter CEO Dick Costolo, leads Square, a growing mobile payments company.
"The Committee will only consider candidates for recommendation to the full Board who are in a position to make a full-time commitment to Twitter," the messaging-platform company said.
"The search is proceeding with a sense of urgency but the Committee will take the time necessary to find the right CEO to lead the next phase of Twitter's growth."
Twitter said it had hired the executive search firm Spencer Stuart to help identify CEO candidates. Costolo announced June 11 he was stepping down amid criticism of the social media company's slowing growth.
Some analysts had speculated that Dorsey, the author of the first "Tweet," might try to lead both Twitter and Square. But Twitter's statement was seen as pressuring Dorsey, who is Twitter's chairman, to make a choice between the two companies.
In mid-morning, trade, Twitter shares fell 0.6 percent to $35.64.
The firm last week announced its acquisition of artificial intelligence startup Whetlab, bolstering the analytics capacity which is becoming increasingly important for social networks.
Terms were not announced for the deal, which was disclosed in a tweet by the Twitter engineering team and on the website of the Massachusetts-based Whetlab.
Twitter did not comment on its plan for the service, but artificial intelligence can be used to determine the most relevant tweets and advertising messages for each user, or to better filter spam.
Written with inputs from AFP
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