The bomb exploded as the bus pulled away from a stop, blowing off the roof and shattering windows on the bus and those of nearby buildings, reports said.
"There was a massive explosion, I couldn't open my eyes. There was black smoke everywhere, there was blood pouring from my head," Ananda Ratnasiri, the bus driver, told AFP news agency.
Mr Hulugalle blamed the Tamil Tigers for what he called a "cowardly attack on civilians".
A police spokesman said 10 people died on the spot and another 14 died while being taken to hospital. A child and a Buddhist monk were among the dead.
Fifty-two wounded people were being treated at two hospitals, the spokesman added.
Witnesses described a large fireball coming out of the bus.
"It is horrible, I saw many people laying on the ground," RB Dharmasiry told the Associated Press news agency.
The remains of the bus
The rebels, who are fighting for an independent state for the Tamil minority, have not commented on the blast.
This is the first attack where there has been major loss of life since 6 April, when a suicide bomber killed 14 people, including a government minister, in the western district of Grampaha.
In February, two separate attacks on buses killed at least 20 in northern Sri Lanka and injured 18 people in a Colombo suburb.
The attack comes as government forces continue a campaign against the Tigers in territory they control in the north of the island.
On Wednesday, the two sides fought a fierce battle in the Jaffna peninsula. The military said it left more than 80 soldiers dead or missing but insisted the rebels had lost even more fighters, as well as their first line of defences.
The rebels said they had repulsed the military's advance and inflicted a defeat on the government forces.
At least 70,000 people have died since the civil war began in 1983.
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