"We call for an independent commission of inquiry to ascertain the reasons why armed officers raided our office," the All Progressive Congress (APC) deputy chairman Lawal Shuaibu told the BBC.
The party said computers were destroyed and documents seized during the raid.
The State Security Service said it was investigating alleged cloning of voter cards, ahead of elections in February.
"The petition alleged that those behind the activities were cloning Inec [Independent Electoral Commission] permanent voters cards, with the intention of hacking into [the] Inec database, corrupting it and replacing them with their own data," the SSS said.
"Based on this information, the Service placed the building under surveillance and having been convinced that some unwholesome activities were going on in the building, it undertook a raid of the premises."
It said its agents had taken away a server, three hard drives and 31 bags of documents on Saturday.
But the APC said the incident was "another one in the string of attacks and illegal actions of the administration".
It said "more than a dozen" computers had been destroyed, a server had been "vandalised" and 28 people arrested.
"Nigerians have been witnessing the way and manner the government have been using force in oppressing us," Mr Shuaibu told the BBC Hausa service.
"This is to be condemned and we have been restraining ourselves from taking actions based on the provocations by the government and the security personnel."
APC spokesman Lai Mohammed compared the raid to the Watergate scandal in the United States, which led to the resignation of President Richard Nixon in 1974.
"Just like the Watergate scandal in the USA, the state-sponsored security operatives apparently acting at the behest of the ruling PDP [People's Democratic Party] government turned the office upside down, and pulled out and vandalised everything in sight," he told the AFP news agency.
The APC has said the office was operating as a "data centre" to process registration of party memberships and was a "legitimate operation".
The APC was formed in a merger of four opposition parties in 2013.
It said there was an urgent need to challenge President Goodluck Jonathan whose party, the PDP, has won every election in Nigeria since the end of military rule in 1999.
The International Crisis Group recently warned that February's election may be "volatile and vicious".
"If this violent trend continues, and particularly if the vote is close, marred or followed by widespread violence, it would deepen Nigeria's already grave security and governance crises," the think tank said.
"The government, its agencies and all other national figures must work urgently to ensure that the vote is not conducted in an explosive situation as this could further destabilise the country."
Nigeria's main opposition party has condemned a weekend raid of its Lagos offices by state security agents.