After Mateen opened fire on some 300 patrons in the gay nightclub in the early hours of Sunday morning, a uniformed off-duty officer engaged in a shootout with the gunman near the club's entrance until backup arrived, Mr Mina said.
Additional police officers arrived at the scene and also began shooting at the suspect, which "forced him to stop shooting and retreat to the bathroom where he had some hostages." Between 15 to 20 people were also trapped in an adjacent bathroom, police said.
Authorities attempted to negotiate with Mateen, but as the negotiations unravelled, and with hostages still trapped inside, a decision was made to breach the wall of the club - first with an explosive device and then with an armoured vehicle.
"There was a timeline given and we believed that there was imminent loss of life that we needed to prevent," Mr Mina said. "It's a tough decision to make knowing that people's lives will be placed in danger by that, our officers' lives would be placed in danger."
He explained the three-hour delay in the SWAT team entering the club (at around 5am, local time) was due to ongoing hostage negotiations and talk of "bombs and explosives".
When police were able to penetrate the wall, Mr Mina said "dozens and dozens" of hostages escaped. Mateen then emerged from the hole in the wall and was shot dead by police.
"We were able to rescue dozens and dozens who came out of that hole," the police chief said.
Officers said the operation "saved many many lives" in the nightclub.
The 11 Orlando police officers and three deputy sheriffs who exchanged gunfire with Mateen are all safe and are relieved of their duties pending an investigation. One officer suffered an eye injury when a bullet struck his Kevlar helmet. The helmet saved his life, special agent Danny Banks said.
Mateen was armed with an assault-style weapon and a pistol. A third weapon was found in his car, authorities said. The US citizen of Afghan descent from Port St Lucie, Florida, had security and firearm licenses and his guns were legally purchased within the past week, even though he had been known to law enforcement for years and interviewed by the FBI three times, federal officials confirmed.
According to Florida law, there is a mandatory three-day waiting period for handgun purchases, but no permit, registration or licensing is needed to buy or own rifles, shotguns or handguns. A permit is needed to carry a handgun.
With grim predicability, the massacre has reignited a war of words over gun laws in the US, with people around the world questioning just what it will take for the country to tighten its firearm laws. But for many Americans, the senseless attack is evidence for why more citizens should be carrying guns.
FBI Special Agent Ron Hopper said police do not believe anyone connected to the shooter poses imminent danger to the public. "We have no reason to believe that anyone connected to this crime is placing the public in imminent danger," he said.
Sunday morning's terror attack on Pulse nightclub in Orlando that left 49 dead and 53 injured is the deadliest shooting in US history.
On Monday, Islamic State claimed responsibility for the attack, saying one of their "soldiers" was able to carry out a "security invasion" at a "crusader gathering". But investigators are yet to uncover any clear links between Mateen and international terrorist groups.
Mateen's father, Seddique Mateen, insisted his son had no Islamist terrorism ties and showed no warning signs the day before the shootings. He said his family is shocked by the "tragic" news.
Mateen's current wife, Noor Zahi Salman, has remained silent since the ordeal began. His ex-wife, Sitora Yusufiy, said Mateen was mentally ill and hit her. She has since gone into hiding and deleted her social media pages.
Around 100 leads have emerged in the ongoing investigation. "No stone will be left unturned and we'll follow the leads wherever they take us," FBI special agent Paul Wyposal told Monday's press conference.
Orlando Mayor Buddy Dyer spoke of the city's resilience in the face of horror. "We will not be defined by the actions of a cowardly hater," Mr Dyer said. "We will be defined by how we respond and treat each other."
President Obama and Vice President Biden are also expected to meet with officials to discuss the ongoing situation in Orlando.
Sunday's tragic events, which coincided with gay pride month in the US, have prompted an outpouring of love and support for the victims and LGBT community around the world. People are turning up in droves to donate blood in Orlando and major cities are lighting up landmarks in red, white and blue or colours of the rainbow flag.
President Obama had to deliver a speech following a shooting for the 18th time and used the event to remind Americans about the need for gun control in an inevitable debate that occurs every time there is a mass tragedy in the country.
"The shooter was apparently armed with a handgun and a powerful assault rifle. This massacre is therefore a further reminder of how easy it is for someone to get their hands on a weapon that lets them shoot people in a school, or in a house of worship, or a movie theatre, or in a nightclub," he said.
"We have to decide if that's the kind of country we want to be. And to actively do nothing is a decision as well."
