"Today, we need to accelerate the elimination of hot spots all over the world, particularly the resolution of the Palestinian issue," Houcine Abassi, the secretary general of the Tunisian General Labour Union, said in an acceptance speech on behalf of the Quartet.
This would be done by giving "the Palestinian people the right to self-determination on their land and (to) build their independent state," Abassi said to thunderous applause in Oslo's City Hall just moments after being handed the prestigious prize.
Abassi said the world was on the one hand "in a great need of dialogue between civilisations, and peaceful coexistence," and on the other it needed "to make the fight against terrorism an absolute priority."
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He denounced the "barbaric and heinous terrorist acts" in recent months in Tunisia, Paris, Beirut, Sharm el-Sheikh and Bamako.
The Quartet is made up of the Human Rights League, General Labour Union (UGTT), the Confederation of Industry, Trade and Handicrafts (UTICA), and the Order of Lawyers.
It was honoured with the Nobel Prize for helping to save Tunisia's transition to democracy at a sensitive moment in 2013 when the process was in danger of collapsing because of widespread social unrest.
The group orchestrated a lengthy and thorny "national dialogue" between the Islamists of the Ennahda party and their opponents.