In a passionate message, Graham Johnston said that "so many people worldwide [are] all hoping and praying for your release". The open letter, which he read out to the media, said: "You have family. Please think about what this is doing to my family. Please let my son go now, today."
The BBC veteran reporter was seized in Gaza a month ago, and in a special international day of action to bring about his release on Thursday, the BBC, al-Jazeera and Sky all agreed to televise the live appeal.
Thanking the BBC, his son's fellow journalists and the Palestinian people for their support, Graham Johnston said: "We are overwhelmed at such support, all of which helps to buoy us up during the past seemingly interminable four weeks."
Direct from the West Bank, the BBC Director General, Mark Thompson, joined the urgent appeal for Alan Johnston's release, BBC News reported.
Thompson met Palestinian Authority President Mahmoud Abbas on Wednesday. He said: "He told me that he had credible evidence that Alan was safe and well. He assured me that Palestinian Authority is fully engaged with Alan's case and working to resolve this as soon as possible."
However, he emphasised that there had been no contact with the kidnappers and no demands had been received. He continued: "It is vital for all journalists to be able to report freely and without fear of harassment and intimidation. The people of Gaza are ill-served by kidnappings of this nature."
Alan Johnston was taken hostage as he returned to his apartment in Gaza City on 12 March - one month ago.
