In a proposition to the parliamentary Foreign Affairs Committee, the minister said they should be recalled from posts.
The committee decided to address the issue at its next meeting and will consider inviting Juška and Žurauskas to attend the session.
"It is a crucial factor that state leaders should have confidence, especially in ambassadors, as they reflect and communicate the state policies, they must enjoy confidence of leadership of the countries, as speaking to ambassadors means indirect communication with state leaders. Under such circumstances, I do not see how they could stay on," the minister told journalists after a meeting of the Foreign Affairs Committee.
"Also, the experience (the ambassadors have) allows them to stay in diplomatic service, however, working in these specific posts would probably be complicated," said Linkevičius.
He emphasized that the ambassadors did not commit an official offense or violation of the law.
The Lithuanian diplomacy chief said the individual who leaked the private conversations have not yet been identified.
"We cannot establish who did it," the minister added.
Linkevičius dismissed the leak as a provocation. In his words, everyone should learn a lesson from the story.
"In today's modern world, information technologies are advanced and make it hard to draw a line between public and private information. Therefore, people who do 'sensitive' work – I am not talking about diplomats and ambassadors only, it also refers to public servants – have to realize that any information can become public. Lesson one – responsible speaking and correct behavior to give fewer reasons for such provocations," Linkevičius added.
In his words, reviewing ways of ensuring safe communication is another lesson.
The minister also emphasized that Lithuanian officials have no experience in handling "sensitive" information.
"There's too much relaxation, we sometimes openly do the things that we should do via safe channels," he noted.
Asked about the international impact of the story, the minister said there should be none.
Benediktas Juodka, chairman of the Foreign Affairs Committee, confirmed on Friday that the panel would gather again to discuss the bid to recall the two ambassadors. He also noted that Juška's four-year term in Hungary is to expire soon.
The investigation into the telephone conversations of Lithuanian ambassadors to Hungary and Azerbaijan leaked on youtube.com was carried out by the Foreign Ministry's Inspectorate General, with additional contribution from the State Security Department and experts.
In the leaked audio recordings, the diplomats share their personal insights on the conflict between Armenia and Azerbaijan, the domestic situation in Turkmenistan and make remarks about Lithuanian leaders.
Shortly after the conversations were leaked last month, Žurauskas turned in a resignation.
Earlier this week, Prime Minister Algirdas Butkevičius said he had lost confidence in the ambassadors.
Under the Constitution, ambassadors are recalled by President Dalia Grybauskaitė upon a proposal from the government.
