"We ask you to bear with us," he said, of the government's unwillingness to share information.
While the mall was a chaotic scene for many hours after the attack began, with people moving in and out of the upscale shopping center, Lenku insisted no terrorists could have escaped.
"Our forces sealed off every point of exit," he said. "It was completely secured."
Earlier Sunday, about 200 Kenyan Muslims held a rally near the mall to remember the dead and call for peace.
"We condemn the terror attack on Westgate Mall," said one sign. "One Country. One People. One Love. Kenya Asia Muslims," said another.
Many of those at the rally were from Kenya's "Asian" community, the descendants of people who came from colonial India what is now India, Pakistan and Bangladesh to work in Kenya more than a century ago.