The message came in response to a video published by fighters of the Islamic State, a jihadist group, on Saturday, which shows beheading of Haines who was abducted in Syria in 2013.
"The brutal and atrocious crime by the ISIS terrorists, just like the recent infamous crimes against US journalists, cannot undermine the determination of the international community and all people of good will in the struggle against terrorism," the Lithuanian ministry said.
The ministry conveyed condolences to the family and loved ones of Haines, as well as all people of the United Kingdom.
"The persons responsible for the crimes must be identified and brought to justice," said the Foreign Ministry, expressing respect to the people who risk their lives in the peaceful professional duties in the zones of armed conflicts.
ISIS fighters recently published recordings of executions of two US journalists.
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