Ignatavičius has worked in Minsk since the spring of 2013.
Pulokas' designation has already been endorsed by the parliamentary Foreign Affairs Committee, BNS reports.
The Cabinet on Wednesday also approved the appointment of Artūras Zurauskas as Lithuania's new ambassador to Latvia. He would replace Ričardas Degutis in the post.
Zurauskas has in the past served as Lithuania's ambassador to China, South Korea, Mongolia and Vietnam and to Greece, as well as Cyprus, Albania and Bulgaria.
He was appointed Lithuania's ambassador to Azerbaijan in 2012, but resigned from the post a year later after recordings of his tapped phone conversations with a colleague were made public. In the recordings, the men exchanged their personal views about the Azerbaijan-Armenia conflict and the situation in Turkmenistan, and made personal remarks about state leaders.
The government on Wednesday also gave the go-ahead for Deputy Foreign Minister Andrius Krivas to take over as the country's ambassador to the United Nations Office and other international organizations in Geneva from Rytis Paslauskas, the current envoy.
Krivas held the post of counsellor at Lithuania's embassy to the United States between 2003 and 2007 and the post of minister counsellor at Lithuania's permanent representation the Organization for Security and Co-operation in Europe from 2010 to 2013, when he was appointed as deputy foreign minister.
Lithuanian ambassadors are appointed and dismissed by the president on the government's recommendation and at the consent of the parliament's Foreign Affairs Committee.
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