Three security force officials, a journalist and another civilian were injured in the attack on Friday in Srinagar, the state's summer capital, police said.
Witnesses said armed fighters first hurled a grenade which was followed by two more blasts and then entered the building, after which they exchanged automatic gunfire with the security forces.
Police said at least one attacker had entered the building, adding that senior Congress leaders were not present when the attack took place.
Two guerrilla groups, al-Mansuran and Kashmir Freedom Force, claimed responsibility for the attack in separate telephone calls to the local Current News Service.
The security forces, backed by armoured vehicles mounted with machineguns, have sealed off all roads leading to Congress office.
In New Delhi, the Congress party expressed outrage. "It is a shocking incident which once again underscores the continuing threat posed by militants to the civil society and the
democratic process," Congress spokesman Anand Sharma told AFP.
"The intelligence and security agencies should have anticipated that militants would do something sensational to attract attention especially after the attacks in Baramula (district) and elsewhere in Kashmir," he said.
On Monday, Srinagar residents will elect a representative from their constituency in the third round of India's staggered parliamentary elections that end on 10 May.
"It is a shocking incident which once again underscores the continuing threat posed by militants to the civil society and the democratic process"
The Congress party is a partner of the regional People's Democratic Party which governs Indian-administered Kashmir.
Separatist and pro-Pakistan groups have waged an insurgency against Indian rule in the majority-Muslim state since 1989 which has cost tens of thousands of lives.
On Thursday, two people were killed and six injured in two separate bomb attacks in Srinagar city.
Separatist rebels have threatened Kashmiris with "unspecified
consequences" if they participate in the elections.
Four people were killed and 25 wounded by rebels in voting in
two constituencies in Kashmir on Tuesday when the elections began.
A senior police officer said extra troops were being shifted to
Srinagar and Budgam districts for Monday's polling.