This marks the second time that the Seimas has rejected President Gitanas Nauseda's veto.
The latest veto was overturned in a vote of 81 to 26 with six abstentions.
MPs say the strategic status is needed to prevent the privatization of the two enterprises.
"What's most important is to protect these companies from privatization," said Valius Azuolas, the chairman of the parliament's Committee on Budget and Finance.
The Seimas Committee on Economics had recommended upholding the presidential veto.
Rimantas Sinkevicius, the committee's chairman, said the prime minister had assured him that the government would halt the privatization of Problematika.
The Seimas added the two companies to the list of Category II enterprises of importance to ensuring national security on October 17.
Nauseda vetoed the decision, saying that Problematika's operations have no strategic importance to national security and that the parliament failed to provided clear arguments regarding Keliu Prieziura.
In August, the Seimas rejected Nauseda's veto on a bill capping at 1.5 hectares the amount of forest land that one owner or a group of related owners can purchase.