"Enemies of Pakistan who want to destabilise the country are coming here after their defeat in Swat," Rehman Malik said.
"There is a war and this is a war for our survival," he added.
There has been no claim of responsibility for the attack but the authorities have been worried about possible retaliation for their offensive in Swat, the BBC's Barbara Plett reports.
Indian Foreign Minister SM Krishna condemned the attack and sent condolences to the bereaved.
"We hope that Pakistan and India would join hands together to fight this terror," he said in Delhi.
UK Foreign Secretary David Miliband condemned the "atrocity" in Lahore and said Britain was "committed to standing shoulder by shoulder with Pakistan in days of need".
'They started firing'
Up to 30 people were killed when the bomb went off mid-morning local time, reports say.
Rob Watson, BBC defence and security correspondent
What is striking about this latest attack, and so worrying for the Pakistani authorities, is the timing and choice of target.
It occurred near the offices of both the local police chief and of the national intelligence agency, the ISI, and comes as the Pakistani military is engaged in a massive campaign against militants in the north-west. So the initial speculation is that this is in some way a revenge attack.
Questions will again be raised about the inability of the authorities to stop the attack altogether given they were clearly expecting reprisals and were on a heightened state after the two other recent attacks in the city.
As to who might have been responsible, the finger of blame is likely to point to the Taliban, although local officials say they have also seen worrying signs in recent times of local Punjabi-based extremist groups working together with militants from the tribal areas to plan attacks in Lahore.
Twelve policemen and a child are among those killed, Pakistani satellite TV channel Geo News reports.
Sajjad Bhutta, a senior government official in Lahore, told reporters that a car carrying several gunmen had pulled up in a street between the emergency response building and the ISI offices.
"As some people came out from that vehicle and started firing at the ISI office, the guards from inside that building returned fire," he was quoted as saying by the Associated Press.
"As the firing continued, the car suddenly exploded."
Issam Ahmed, a journalist with the Dawn newspaper in Lahore who arrived at the scene about 20 minutes after the blast, told the BBC he could still hear shooting in the area.
A least two arrests were made.
Rescue workers were seen clambering over a pile of concrete which was all that remained of the emergency response headquarters.
They were able to drag out several of the injured. Semi-conscious policemen could be seen being carried out in blood-stained uniforms.
Debris was scattered on the road outside. Officials were seen rushing towards the buildings to cordon off the area.
The blast also destroyed several cars parked or standing on the main Mall Road opposite the police building.
Bulldozers and other heavy lifting equipment were brought in as many people were feared trapped under the debris.
Distraught women could be seen looking for news of missing relatives.
Zubair Bukhari, a BBC News website reader in Lahore, described hearing the explosion: "I was sitting in my office on Lawrence Road [about 500m from the site] when a huge explosion rocked our entire building.
ATTACKS ON LAHORE THIS YEAR
3 March: Gunmen kill six police guards in an ambush on the Sri Lanka cricket team
30 March: Gunmen attack a police academy, killing eight people
27 May: A car bomb attack on police buildings kills at least 23
"Glass windows shattered to pieces and the ceiling came down on the floor. I ran outside the building to nearby Jinnah Garden. I could hear gunfire which lasted for about 10 minutes and then I saw ambulance and police rushed to the scene."
Matthias Gattermeier, an Austrian reader also in Lahore, said his office building had been shaken so hard he thought it would collapse.
"We first thought the explosion happened far closer by, but the blast was just so massive," he said.
"I ran out of the building and saw a surreal huge ring of white smoke rise into [the] air. Within minutes police and military blocked the streets. Disaster units and emergency are going in and out every minute. The streets are full of people."
In previous attacks, a Lahore police college was attacked on 30 March with eight people killed, and weeks before that militants attacked the Sri Lanka cricket team in the city, killing six police guards.
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