The amendments are being tabled after the Seimas upheld in September President Dalia Grybauskaitė's veto of the reform package approved by the parliament earlier this year.
Veryga says the amended legislation will set the same criteria for public and private hospitals for being included in the network and signing agreements with Territorial Health Insurance Funds (THIFs) for the costs of health services to be covered by the Compulsory Health Insurance Fund.
The proposed criteria include providing 24-hour emergency services and offering a range of services, as well as geographic accessibility.
The network would be approved by the government, rather than by the health minister as provided for by the vetoed legislation, and would be reviewed every five years.
The new rules would come into force in 2020.
Under the previous amendments, private in-patient care facilities would have been able to conclude contracts with THIFs only if they provide services that cannot be ensured by public hospitals.
Grybauskaitė sent the reform package back to the Seimas, saying that the provision might run counter to the Constitution in that it would give state-owned hospitals priority access to compulsory health insurance funds and would thus limited patients' choice.