Mr Johnston was in the last weeks of his posting when his abandoned car was found on a Gaza street on March 12th.
Earlier this month a previously unknown militant group calling itself al-Tawhid al-Jihad Brigade contacted news agencies to claim it had killed the 44-year-old.
But following a lack of independent verification, Mr al-Ahmad said today: "The information that we have indicates that [Mr] Johnston is in good health.
"The [Palestinian] government is fully co-ordinating with the presidency and all security services to pursue the extensive efforts to release [Mr] Johnston and bring him back safely to his home, family and his work."
More than 50,000 people have registered their names in support of Mr Johnston on a BBC website petition, while journalists across Europe and the Middle East have staged demonstrations demanding his immediate release.
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