Dozens of workers fled the office on Thursday as security forces surrounded the building with the fighters holed up inside. One was later killed, officials said.
"I have rescued about 100 people. There are many still trapped inside," said police officer Shafi Bhat, who drove an armoured truck into the compound to ferry out government workers and other civilians. It was not clear, however, if anyone was being held hostage.
Scores of relatives of office workers flocked to the scene as word of the siege spread through the city.
Office workers were forced to
flee the building during the siege
The attack began at about 2.00 pm (0830 GMT) when at least two men firing automatic weapons forced their way into the administrative complex in central Srinagar, killing two soldiers on guard at the entrance, said Neeraj Kumar, a paramilitary official. One civilian and one of the fighters were later killed.
Police, civilians injured
Five policemen and four civilians were also injured, said H K Lohia, a police official.
Shortly afterward, security forces surrounded the complex and began manoeuvring armoured vehicles into position to help with the rescue.
"All we could hear were firing and explosions. Then some policemen huddled us into a truck and we were driven out," said government worker Ghulam Qadir.
Hundreds of people work in the building, the headquarters for the Srinagar district government, located in an old palace on the banks of the Jhelum River that flows through the summer capital of Jammu and Kashmir state.
Security forces surrounded the
complex, trying to resuce workers
In a separate incident, soldiers raided a suspected rebel hide-out 70km north of Srinagar late on Wednesday, sparking an all-night gun-battle that left at least two dead, said Lieutenant Colonel V K Batra, an army spokesman.
Soldiers were searching the area for more fighters, he said.
There were no casualties among security forces, he added.
More than a dozen armed groups have been fighting security forces in Indian-administered Kashmir since 1989, seeking independence for the Himalayan region or its merger with neighbouring Pakistan.