SAN FRANCISCO — Twitter’s chief operating officer, Ali Rowghani, resigned on Thursday, after months of watching his responsibilities shrink.

The social networking company said in a securities filing that it did not intend to appoint anyone else to the position.

Mr. Rowghani, who joined Twitter in 2010 as chief financial officer, ascended to the No. 2 spot a couple of years later. Although his duties varied, he had recently overseen efforts to expand the service by attracting new users and increasing activity among existing users.

But those efforts failed to bear fruit, and Twitter’s stock plunged from more than $70 last December to around $35 before the news of Mr. Rowghani’s departure. It rose 3.5 percent to $36.79 on Thursday.