Story highlights Sen. Al Franken said he would resign in a "couple of weeks"

Through Senate rules, his replacement could start as soon as Friday

Washington (CNN) Even though he announced he would resign within "the coming weeks" amid accusations he groped women, Sen. Al Franken is still reporting for duty to Capitol Hill with no departure date set.

Gov. Mark Dayton, a Minnesota Democrat, said Wednesday that Minnesota Lt. Gov. Tina Smith was appointed to a one-year term in the Senate , which will conclude in January 2019. Smith, thought to be a leading contender to replace Franken, accepted the appointment.

But since his resignation last Thursday, the Minnesota senator has cast five Senate votes, attended at least one committee hearing as of Thursday and gave a floor speech on net neutrality Wednesday afternoon.

And while his replacement has been set, the senator's office has said he does not yet have a departure date -- and is still finalizing his plans.

His office told CNN his resignation date was still being "finalized" on Wednesday. And when pressed by CNN four times about his resignation on Thursday, Franken declined to answer questions on why he hadn't set his date.

Read More