Nicaragua's arguments in the border dispute include a map of Costa Rica without the Nicoya peninsula, claiming that the maritime limits disputed before the ICJ should not take that territory into account.
Nicaragua will have until June 2 to submit a response. Justices then will issue a final ruling on the damage compensation figure and on a deadline to make the payment.
Costa Rica asked the International Court of Justice to add a new complaint against Nicaragua to an ongoing case of a border dispute first filed in 2014.
The deadline for Costa Rica and Nicaragua to reach an agreement on the payment of compensation over environmental damage ruled by the International Court of Justice (ICJ) ended Friday without any signs of a settlement.
Foreign Minister Manuel González Sanz said Costa Rica's decision to walk out of the U.N. General Assembly before Brazilian President Michel Temer's speech has been blown out of proportion.
Paving the way for a possible visit by U.S. President Barack Obama to Costa Rica later this year, Costa Rican Foreign Minister Manuel González met last Thursday with his U.S. counterpart, Secretary of State John Kerry, for the first time since the May 2014 inauguration of President Luis Guillermo Solís.