Nearly all of the witnesses in the House impeachment inquiry have testified behind closed doors, drawing attention—including objections—to the process Democrats are using to explore whether to remove President Trump from office.

The investigation into Mr. Trump’s effort to have Ukraine investigate former Vice President Joe Biden, a candidate for the Democratic presidential nomination, is taking a different path so far than the three previous presidential impeachments. That has prompted accusations from Republicans that Democrats are keeping secret the information they are gathering.

“You know who’s not invited to these meetings ... the American people,” House Minority Whip Steve Scalise said this week on Fox News Channel. He accused House Intelligence Chairman Adam Schiff (D., Calif.) of “trying to hide from the American people what’s really going on behind these closed doors.”

Democrats counter that the inquiry, which is being conducted by three House committees, is in its early, fact-finding stage. They point to previous House investigations that have had closed-door depositions and said they intended to make the testimonies public.

House Speaker Nancy Pelosi (D., Calif.) has set no time limit on the investigation and said Thursday that “the timeline will depend on the truth line, and that’s what we’re looking for.”