BUDAPEST — Rescuers were fighting the currents of a flooded Danube river on Friday in search of survivors and of the wreck of the sightseeing boat that sank in the center of Budapest two days ago. But Hungarian officials offered little hope that any of the 21 people still listed as missing would be found alive.

Prime Minister Viktor Orban of Hungary spoke on Friday of his distress at the sight of an accident “where passengers had almost no chance for survival.” He promised a thorough investigation into the boat accident, which left seven people confirmed dead.

“We want to know precisely what happened and why it happened,” Mr. Orban told Kossuth, the state radio station, adding that the authorities would reveal their findings in due course.

The accident happened when the Mermaid, a sightseeing boat, was apparently clipped by the Viking Sigyn, a Swiss-operated river cruise ship, in heavy rain.