According to Icelandic authorities, the search was discontinued after the tour operators' registers were examined and it was established that all 23 people on the tour were identified.
The police had previously initiated a search for two people who were believed to be missing, since they had initially received information that there had been 25 people on the expedition.
One person died in the accident when the ice cave in the Breidamerkurjökull glacier on southeastern Iceland collapsed on Sunday afternoon, according to Icelandic Rúv. Another person was seriously injured. The deceased was an American citizen, according to the AP news agency. The injured person is also an American citizen.
The cave is a popular tourist destination and most of the visitors were outside the entrance at the time of the accident.