The Catalans are asking for an additional 10 percent payment due to a delay in their demands being met.
"Barcelona have taken these actions in defence of their interests, after Neymar's contract was rescinded just a few months after he signed on until 2021," a club statement said.
Brazilian striker Neymar, who joined PSG earlier this month after the French club triggered his 222 million euros release clause, said he was surprised by the decision but warned he was not going to give in.
"It is noteworthy that this news was received with surprise, since the athlete completely fulfilled the contract then in force, with the full deposit of the amounts set out in the buy-out clause freely agreed with F.C. Barcelona for his release," Neymar's representatives said in a statement.
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The statement added that the 25-year-old forward's lawyers were preparing a formal defence to the demands.
PSG activated Neymar's release clause as Barcelona were unwilling to negotiate the sale of one of their best players.
Barcelona have passed the complaint to the Spanish football federation (RFEF) after first filing the lawsuit in court, as well as demanding PSG subsidise it, should Neymar not be able to take responsibility for it.
PSG brushed off that suggestion and said they had done all that was required of them.
"Paris Saint-Germain reiterates that, like Neymar Jr., it has always respected all applicable laws and rules in its dealings and, once again, regrets the attitude of FC Barcelona," the club said in a statement.
In the days after he signed for the French club, Barcelona refused to pay the reported 26 million euro instalment of the loyalty bonus which he was due to receive this summer, citing breach of contract.
On Sunday, Neymar criticised the Barcelona board after helping PSG beat Toulouse in Ligue 1.
"I am disappointed with them (Barcelona directors). I spent four very happy years there and left happy, but not with them. For me they shouldn't be in charge of Barcelona. Barca deserve much better and everyone knows this," Neymar said.
(With additional reporting by Andrew Downie; Editing by Christian Radnedge and Pritha Sarkar)
