Johnston, 44, was seized at gunpoint as he drove home from work in Gaza City on March 12.
One of the few Western reporters to have both lived and worked in Gaza, he has become the longest-held kidnapped Westerner in the territory.
On Sunday, an Islamist group called the Kataeb al-Jihad al-Tawheed (The Brigades of Holy War and Unity) claimed in a statement to have killed Johnston.
However, Palestinian authorities say there is no proof that the claim by the little-known group was true.
Barghouti was a key figure in the early days of the second intifada (uprising) that began in September 2000.
He was convicted by Israel in May 2004 on five counts of murder and one of attempted murder resulting from three suicide attacks and one failed attack, and is currently serving five life sentences.
Barghouti still has popular appeal among Palestinians, with many insisting that the charges against him were false and motivated by politics.
In January 2006 he was re-elected to the Palestinian parliament and he is widely seen as a possible successor to Abbas, the current president and leader of Fatah.