Mark Thompson, the director-general of the BBC, called on Johnston's captors to release the journalist in a press conference in Ramallah.
"I appeal to all those who may have influence with the kidnappers to use their best endeavours to secure Alan's release safely and speedily."
Thompson said that at a meeting with Mahmoud Abbas on Wednesday, the Palestinian president had told him: "that he had credible evidence that Alan was safe and well."
Richard Porter, head of news at BBC World, said in a statement: "We don't think this has ever happened before."
"All the broadcasters involved share a common aim to highlight Alan's case and to remind viewers of the dangers faced by their news teams more frequently than ever."
Steve Clark, director of news and programmes at Al Jazeera English, said: "We at Al Jazeera stand firmly alongside the BBC and other broadcasters of the world in condemning those who abduct or attack journalists pursuing their profession.
"We hope this unique programme will help highlight and resolve the problems we all face."
Palestinian journalists have also held a three-day strike to press their government to do more to secure Johnston's release.