Mr Johnston, 44, disappeared last week after he was reportedly snatched by four masked gunmen in Gaza City.
Margaret Beckett, the Foreign Secretary, yesterday told MPs said she had raised the issue with Mahmoud Abbas, the president of the Palestinian Authority.
"I'm assured by President Abbas that it is very much a goal of the Palestinian government and authorities," she said. "It's extremely important that we try to secure this and I think it is particularly sad ... when someone who has been a long-standing friend of the people of Palestine suffers in this way and it does nothing to help."
Palestinian journalists in the Gaza Strip went on a 24-hour strike yesterday in protest at the abduction.
The Palestinian Journalists Union said that it could "escalate" such protest actions unless Mr Johnston, who was educated at Dollar Academy and Dundee University, was released forthwith.
The union called the strike a "protest against the continued status of negligence, carelessness and silence" in Gaza, which has seen spiralling criminal and factional violence since Israel withdrew troops and settlers in 2005 after 38 years of occupation.