The government is seeking $44bn in compensation for the costs of treating smoking-related diseases.
The firms are also accused of deliberately trying to promote smoking among young Nigerians.
The firms, British American Tobacco, Phillip Morris and International Tobacco deny all charges.
Lawyers representing Phillip Morris were not in the Abuja court. Government lawyers said they had refused to accept their summons.
The BBC's Alex Last in Nigeria says this lawsuit is likely to take quite some time.
The federal government case follows the decision of Nigerian state governments to sue the tobacco firms for billions of dollars.
We haven't got a clue where the government got the amount they are asking for
Catherine Armstrong, BAT
Nigeria takes on tobacco giants
They hope to follow the model of states in the US, who sued big tobacco in the 1990s and then settled out of court for billions of dollars.
Our correspondent says the actual amount sought in compensation by the Nigerian government is considerably more than the entire federal budget.
Cynics say the government has never spent anywhere near that amount on health care - which is in a state of collapse because of decades of mismanagement and corruption.
But anti-smoking campaigners and some civil rights groups have welcomed the decision to sue.
For decades, tobacco firms have been accused of aggressively targeting Africa as a market, to offset the impact of tougher anti smoking regulations introduced in the west.
Source: BBC
