Cruz said Magtibay was the ground commander and had taken responsibility for the incident, while four special weapons and tactics (SWAT) team leaders had been ordered on leave pending an investigation.
A day earlier, government officials said there had been "defects" including poor handling of the negotiations, and that the assault team was inadequately trained, equipped and led.
Police on Wednesday confirmed three of the dead as Canadian citizens.
Philippines officials promised a full investigation into how the hostage-taker armed with a M16 rifle and a pistol was able to gun down eight of the 15 hostages on board the bus before he was killed by a sniper.
Rolando Mendoza, the 55-year-old who hijacked the tourist bus, was a dismissed former police officer demanding his job back. He was eventually shot dead by police.
The official acknowledgement of "inadequacies" in the police's handling of the situation came amid public outrage in Hong Kong.
Jessie Robredo, the Philippine interior secretary who is in charge of the national police, on Tuesday acknowledged there were problems with how the crisis was handled.
"Had we been better prepared, better equipped, better trained, maybe the response would have been quicker despite the difficulty"
Jessie Robredo, the Philippines interior secretary
"Had we been better prepared, better equipped, better trained, maybe the response would have been quicker despite the difficulty," Robredo said.
"All the inadequacies happened at the same time," he added.
Police had defended their actions saying that officers lacking proper equipment had risked their lives in trying to bring the standoff to an end.
But they promised to review all events leading to the deaths.
Benigno Aquino III, the Philippine president, declared Wednesday a national day of mourning in solidarity with the people of Hong Kong to "share their sorrow", Edwin Lacierda, his spokesman, said.
In Hong Kong, a semi-autonomous Chinese territory, sorrow quickly evolved into outrage with several political parties leading protesters to the Philippine consulate.
Demonstrators chanted "You caused the deaths of Hong Kongers".
"We think the Philippine government used the wrong strategy," Lau Kong-wah, pro-Beijing legislator, said.
"We think the operation failed," he added.
Several Hong Kong newspapers printed mastheads in black, and flags in the territory flew at half-mast.
"Filipino police incompetent", read the front-page headline of Hong Kong's Ming Pao Daily News.
There is also fear of retaliation against a huge Filipino community in the territory.
Hong Kong-based Asian Human Rights Committee, in echoing calls for an explanation of the incident, said it was "deeply concerned by people who are trying to blow this incident out of proportion".
|Demonstration and harsh words in Hong Kong marked public outrage over the incident [EPA]
It cautioned that such anger might see retaliatory attacks against thousands of Filipinos who work there, mostly as maids.
"This tragedy should not become a conflict of nationalities," the committee said in a statement.
On Tuesday Aquino, facing his first major crisis since taking office on June 30, met Liu Jianchao, the Chinese ambassador, and phoned Donald Tsang, Hong Kong's leader, to brief them on the investigation.
The ordeal ended in bloodshed on live television with police storming the bus and killing Mendoza after he fired at the tourists.
Of the 25 people originally on the hijacked bus, 13 of the Hong Kong tourists and four Filipinos survived.
Mendoza had freed nine of the survivors, including two British nationals, hours before the gunfire began.
Among the victims were a mother of three who lost her husband and two daughters and a teenager oblivious of her parents' death.
Amy Ng mourned the deaths of her husband Ken Leung, whom she said confronted the gunman, and daughters Doris and Jessie, aged 21 and 14.
Her son, Jason, was still hospitalised after an operation on a head wound.
"I thought I would fight for survival so I could take care of my children, but two of them have already died," she said.
Tracey Wong, 15, who was bedridden, said she hid under a seat in the bus while Mendoza fired at the hostages.
"I want to find daddy and mommy quickly and see if they're OK," the teenager said, not knowing that her parents have been reported killed.
Hong Kong has since cancelled tours to the Philippines and asked Hong Kong tourists still in the country to leave.
Philippine officials say about 140,000 Hong Kong tourists visit the country annually.