Since Mr Johnston went missing in the troubled region on March 12th the Palestinian authorities insist they have instructed security services and the interior ministry to undertake "all necessary measures" which will ensure Mr Johnston safe release, the BBC says.
Leading media figures such as David Dimbleby, Sir David Frost, Jon Snow and Christiane Amanpour of CNN have also demanded the release of Mr Johnston and increased pressure upon the Palestinian authorities to find him and secure his release.
However today a London-based Arab language newspaper, Al-Hayat, reported that Palestinian security forces are looking into the possibility that Mr Johnston staged his own capture, according to the Jerusalem Post.
The archbishop of York Dr John Sentamu also called for the journalist's release in his Easter sermon yesterday.
Speaking about a "fear of 'the west'", Dr Sentamu said this fear had "played its part in the horrendous kidnap" of Mr Johnston.
"In God's name please release Alan Johnson. He is not your enemy. He is a symbol of ensuring that freedom of the press is not violated – an issue Palestinian journalists are too familiar with after facing routing attacks, harassment and arrests."
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