Motuzas was recalled to Vilnius for consultations last week. The decision will be reviewed this week.
"The status does not preclude him from representing our country in Moscow. Moreover, given the procedures, the ambassador's role or influence in issuing visas is very symbolic and minimal," the prime minister told reporters.
"Today I see no formal reason preventing the ambassador to Russia from continuing his work," he added.
The status of a special witness means that a person is questioned about his or her actions but there are no grounds to bring formal suspicions against him or her.
Formal suspicions of influence peddling have been brought in the case against Rimantas Sidlauskas, a former long-standing Lithuanian diplomat, Rinat Nasirov, a Russian banker, and Albinas Bieliauskas, a Lithuanian businessman.
Sidlauskas is suspected of taking a bribe in exchange for his promise to help Nasirov obtain a long-term Schengen visa.
The Lithuanian embassy in Moscow issued Schengen visas to Nasirov and his son in late March, based on an invitation letter from by Sidlauskas.
The ambassador confirmed that Sidlauskas had informed him about his plans to send the document.
President Dalia Grybauskaite said last week that Motuzas was becoming vulnerable and cast a shadow on the diplomatic service as a whole.
The prime minister says no status in a pre-trial investigation indicates "that a person is guilty or has violated the law".
"We are a state ruled by law, but we often prejudge a person guilty," he said.
Motuzas has served as Lithuania's ambassador to Russia since 2015.
Lithuanian ambassadors are appointed by the president on the government's recommendation and with approval from the parliament's Foreign Affairs Committee.