In a declaration issued after their meeting in Lithuania, the prime ministers also underlined that the door remains open for a Polish company to participate in the project.
"The prime ministers encouraged the companies to finalize the negotiations in timely manner, to put signatures un the concession agreement by June 2012, which would enable the process to move to the next stage," the declaration said.
The concession agreement is to be signed by Lithuania's government and US- Japanese company Hitachi-GE Nuclear Energy, chosen as a strategic investor. Representatives of the Lithuanian government say representatives of a new company being established for the project should also attend the signing.
Lithuanian Prime Minister Andrius Kubilius refused to elaborate but an initial shareholder agreement is expected to be also signed by June.
The head of the Lithuanian government also said energy companies of the three countries had indicated the amounts of energy they hope to get from the Visaginas nuclear power plant. But the prime minister did not say exactly how the shares would be divided.
"The companies indicated what amount of power they hope to get from the Visaginas nuclear power plant. It clearly shows us that there are no major disagreements or problems on that," Kubilius told journalists at a joint press conference with his Latvian and Estonian counterparts Valdis Dombrovskis and Andrus Ansip.
The Estonian prime minister said his country would like to get 300 mega-watts from the new utility, which is projected to have total capacity of 1,300 mega-watts. In Ansip's words, the country currently generates enough energy to satisfy its needs but seeks diversification of resources.
"There is still need to diversify our energy production. This is the reason why we would like to cover 300 mega-watts of our energy consumption with the electricity produced in Visaginas Nuclear Power Plant," the Estonian PM told journalists.
Latvia's Dombrovskis restated his country's interest in the project but refused to specify the share that would be of his country's interest.
"I would also like to reconfirm Latvia's commitment to this project and the progress, which has been made by our energy companies in negotiating this project," Dombrovskis said.
Lithuania hopes to build the new nuclear power facility by 2020, with the help of Hitachi and Latvian and Estonian energy companies.
Polish company PGE announced last December it decided to withdraw from the project. But the Baltic states say the door remains open.
"We are keeping open the possibility for the Polish company to decide and take part in the project," Kubilius said.