Twitter said Monday it would only consider chief executive candidates who can commit full-time to the company, signaling that co-founder and interim head Jack Dorsey likely will not be picked.

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.