Fourteen of the missing have been found alive and seven bodies were in the morgue, it said.
The government has said 67 people were killed after al-Shabab militants stormed the Westgate centre in the capital, Nairobi, on 21 September.
MPs have started a probe into alleged intelligence failings over the attack.
The Red Cross says some relatives were not updating them when they found people who had been reported as missing.
A Red Cross tracing manager has told the BBC that “some were reports from people who could not get through to their relatives on the phone and thought they might have been at the mall”.
The organisation has been calling those who reported people missing for updates.
Five militants were killed by the security forces during the four-day siege and 10 people have since been arrested, the authorities say.
Al-Shabab, a Somali Islamist group, said the attack was in retaliation for Kenya’s military involvement in Somalia.
Security sources have told the BBC that the militants hired a shop at Westgate in the weeks leading up to the siege.
Kenya’s joint parliamentary defence and national security committees met briefly on Monday morning to begin their investigation into possible lapses in the country’s security system.
They have now adjourned and plan to visit Westgate later on Monday. They will start calling people on Tuesday to testify before the joint committees.
Committee head Ndung’u Gethenji had said the questioning of the security chiefs, including the head of the National Intelligence Service (NIS), Michael Gichangi, would begin on Monday.
He told the BBC last week that “people need to know the exact lapses in the security system that possibly allowed this event to take place”.
He also said they needed to understand “the anatomy of the entire rescue operation” amid allegations of confusion over who was in charge.
Kenyan newspapers have reported that the NIS warned a year ago of the presence of suspected al-Shabab militants in the capital and that they were planning suicide attacks, including on the Westgate shopping centre.
Briefings were given to the ministers “informing them of increasing threat of terrorism and of plans to launch simultaneous attacks in Nairobi and Mombasa around September 13 and 20, 2013”, Kenya’s Daily Nationhad quoted counter-terrorism reports as saying.
A dossier from the NIS – amounting to more than 8,000 pages according to Kenya’s Standard newspaper – also suggests the Israelis issued warnings that buildings owned by its citizens could be attacked between 4 and 28 September.
Westgate is partly Israeli-owned.
The Daily Nation has reported that Kenyan intelligence had established that al-Shabab leaders had begun singling out Westgate and the Holy Family Basilica for attack early this year.
Government figures said to have received the intelligence briefings include Interior Minister Joseph Ole Lenku, Treasury Minister Julius Rotich, Foreign Affairs Minister Amina Mohammed, Defence Minister Raychelle Omamo and Kenya Defence Forces chief Julius Karangi.
On Sunday, Mr Lenku refused to answer questions on the issue, saying the information was confidential and would not be discussed in public.
However, a senior interior ministry official earlier denied that ministers had ignored intelligence warnings.
The official – who was speaking on condition of anonymity – told the BBC the government received intelligence daily, that action was taken and that many attacks had been averted.