Interior ministry spokesman Zemarai Bashary said the three were 'robbers or thieves', say media reports.
"We don't know whether these are Taliban or insurgents because when they entered the bank, they must have intended to steal," Mr Bashary said.
He also said that the police was able to get to them quickly and get the situation under as it was in the center of the city.
On the other hand, the spokesman for the Taliban, Zabihullah Mujahed claims that in the gubattle launched by the militants against the police a dozen police personnel have been killed, says a news agency report.
This is the third attack this week, as the militants have vowed to disrupt the presidential elections which is all set to begin on Thursday, Aug 20.
The first attack took place on Saturday, Aug 15 when a bomb was detonated in front of the NATO headquarters that killed at least seven and injured scores. On Monday, Aug 18 two rockets were launched into Kabul. One of the rockets struck the presidential palace while the other targeted at a police station near by.