Minister says it is possible people are reporting the missing to the Red Cross and not to the police

More than three dozen people remain unaccounted for almost a week after the end of the four-day terrorist attack on Nairobi's Westgate mall which killed at least 67, the Kenyan Red Cross has said.

The Red Cross's report of 39 missing people conflicts with the government's contention that there are no remaining missing people from the attack that began on 21 September, and suggests that the death toll could still rise as investigators dig through the rubble of the partially collapsed mall.

"The numbers with us are what we are still showing as open cases that are reported to us," said Abbas Gullet, head of the Kenyan Red Cross. "The only way to verify this is when the government declares the Westgate mall 100% cleared – then we can resolve it."

At least 61 civilians and six security troops were killed in the attack. Government reports on the number of terrorists killed have been confusing and at times contradictory.

The president, Uhuru Kenyatta, said last week that five attackers had been killed by security forces' gunfire, and his office said one or more might be trapped under the building's rubble.

In an interview on Citizen TV late on Sunday night, however, the interior minister, Joseph Ole Lenku, said two attackers had been hit by gunfire and that the building was thought to have collapsed on three others.

Later in the interview he said all five Islamist attackers were thought to be under the rubble, and that no bodies of any terrorist suspects had been recovered. "We are sure they never got out of the building, so let the forensic examination establish the exact truth," he said.

When pressed about the government's initial estimate that 10 to 15 terrorists could have been involved in the attack, Lenku conceded that the figure could have been wrong, or that some could have escaped.

"We do not rule out the possibility that when we were evacuating people in the first stages of the operation it is possible some could have slipped out," he said. "And that is why we are holding a number of people for interrogation; that is why we immediately sealed off the points of exit, the airports."

Gullet said the Red Cross number of missing had been dropping over the past week as bodies had been positively identified and as some missing people had been reunited with their families. On Friday the Red Cross said the number of missing people stood at 59.

The Nairobi city morgue said it had no remaining bodies recovered from the Westgate attack as of Friday.

On Sunday Lenku said police had no missing persons reports from the mall attack, and that authorities did not believe there had been any hostages in the mall building when it partially collapsed.

He left open the possibility, however, that things might change. "We think – unless the forensic investigation shows otherwise – we really do think that there were weren't any hostages," he said.

In the television interview later on Sunday, Lenku indicated it was possible that people were reporting the missing to the Red Cross and not to the police. "Why is this not being reported to the police?" he asked. "Kenyans must learn to use the government machinery to do their report."

Investigators from Britain, the US, Canada and Germany are participating in the investigation into the attack and are aiding Kenyan forensic experts poring through the mall complex. Results are not expected until later this week at the earliest.

Kenyan authorities have detained a total of 12 people in connection with the attack, including one on Sunday. Three people have been set free, including a British man who was reported to have been arrested last week as he tried to board a flight from Nairobi to Turkey with a bruised face, Britain's Foreign Office said.

The militant group al-Shabaab has said it carried out the mall attack to punish Kenya for sending its troops into neighbouring Somalia to fight the al-Qaida-linked militant group, which had seized large parts of that country for years before being dislodged from the capital, Mogadishu.