The claims were filed in the end of office hours on Tuesday, the court confirmed.
"Both claims were received," Jolanta Talutienė, adviser to the court chairman, told BNS.
The former FCIS officers also asked the court to suspend the competition for the top FCIS position.
Palaitis dismissed the two top officials of the Financial Crime Investigation Service, Vitalijus Gailius and Vytautas Giržadas, on 15 February, after a recommendation from the State Security Department. The department was investigating possible leak of information about Snoras bank shortly before its nationalization.
Shortly after the sacking, the Interior Ministry announced a competition for the vacant post. One application has been received, and the competition should take place on Friday.
Prime Minister Andrius Kubilius has dismissed the sacking as a mistake and asked the government to revoke the minister's decision.
Meanwhile, Lithuania's government was discussing the bid to revoke Palaitis' decree concerning Gailius and Giržaas.
The government recommended the Ministry of Interior Affairs to halt the competition for a new chief of the Financial Crime Investigation Service, Prime Minister Andrius Kubilius told journalists on Wednesday.
The ministers also agreed to start restructuring the FCIS.
The Cabinet also discussed a possibility to cancel Minister of Interior Affairs Raimundas Palaitis' decisions to dismiss FCIS director Vitalijus Gailius and his deputy Vytautas Giržadas, but no decision was made on the issue, Kubilius said.
Meanwhile Palaitis told journalists he was ready to halt the competition. He said the decision would be "rational" if "structural reforms are carried out fast."
Palaitis also underlined that Gailius and Giržadas could not be reinstated as they had lost the right to work with classified information.