"The Justice Ministry will in the coming days send a letter to the Russian Justice Ministry regarding the execution of the request submitted in 2016," Audris Kutrevičius, the ministry's spokesman, told BNS.
The ministry in 2016 asked for Mataitis to be transferred to Lithuania to serve his sentence based on a bilateral agreement, but has received no answer from Russia yet, he said.
Seimas Ombudsman Augustinas Normantas initiated the meeting after Mataitis' sister, Jolanta Stonienė, asked him to mediate in bringing her brother, who is held in a Russian prison, back to Lithuania.
Following the meeting, Normantas asked the Justice Minister to inquire about the results of the examination of the 2016 request, Vytautas Valentinavicius, spokesman for the Seimas Ombudsmen's Office, told BNS.
A Kaliningrad court in 2016 sentenced Mataitis to 13 years in prison for spying. Aristidas Tamosaitis, a Lithuanian citizen, was convicted of spying by a Moscow court in the same year.
The men were detained after Lithuanian law-enforcement officials arrested Nikolai Philipchenko, a Russian national, on spying charges.
A Lithuanian court later said that Philipchenko was an officer of Russia's Federal Security Service (FSB), and sentenced him to 10 years in jail.
Mataitis' sister told the Lietuvos Rytas TV station that she had asked the justice minister to "swap two people serving prison sentences in different countries".
Lithuanian officials would not comment on the possibility of a swap.