Hopes rose for the safety of kidnapped BBC journalist Alan Johnston yesterday as his parents issued a plea to his captors for his release.

His parents, Graham and Margaret, travelled from their home in Lochgoilhead, Argyll, to London where they read out an open letter to their son and his captors, in which they urged him to keep his "chin up".

Posters pressing for the reporter to be freed were unveiled in Glasgow, London and Edinburgh yesterday, and a programme about Mr Johnston was broadcast on television.

Mr Johnston disappeared on his way home from his Gaza City office on March 12 and his car was found abandoned amid reports he was snatched by masked gunmen. Hopes that the journalist would be freed rose after BBC director general Mark Thompson was told by Palestinian President Mahmoud Abbas that Mr Johnston was "safe and well".

He promised Mr Thompson the authorities were "fully engaged" in trying to secure his freedom. Mr Thompson cut short a holiday to the Middle East as part of a day of action by the BBC calling for Mr Johnston's release. Mr Thompson said of his meeting: "He told me that he had credible evidence that Alan was safe and well. He assured me that Palestinian authorities are fully engaged with Alan's case and working to resolve this as soon as possible."

The journalist's parents wrote the letter to their son which Graham Johnston, 74, read out. It said: "Hello old son, I don't know if you will see this but I just felt that I wanted you to know how distressed and sorry we all are that you were taken. You had warned us frequently that the chances were always there that you would be kidnapped, and we were prepared in a way for this to happen. Nevertheless, when it came it was a considerable shock."

Mr Johnston told his son not to worry about his family, and said his parents and sister Katriona were trying to keep a "stiff upper lip". He spoke of the "phenomenal" support they had received from friends and colleagues home and abroad.

The letter continued: "There are so many people worldwide all hoping and praying for your release, not least of which I am sure are the vast majority of the Palestinian population, many of whom have told us they are ashamed that you were kidnapped. There is so much sympathy for your plight around the globe and we are overwhelmed at such support, all of which helps to buoy us up during the past seemingly interminable four weeks."

Mr Johnston also had a message for his son's captors: "You have families.

Please think about what this is doing to my family, including in particular the distress and deep, deep concern Alan's mother and sister have had to endure for all these long weeks. As I have said before, please let my son go now - today. Alan, all our heartfelt, warmest, fondest love is sent to you from all your family in the fervent hope that you will be released unharmed. Chin up, my son."

Helen Boaden, the BBC's director of news and current affairs, said the comments from President Abbas gave the first credible evidence that Mr Johnston was safe. She said it was "very good news", but it did not diminish the concern felt by Mr Johnston's family and colleagues. She also paid tribute to Mr Johnston, saying he was a great journalist and broadcaster, and an "incredibly decent man". "Above all, he is our boy and we want him back," she added.

Ms Boaden said the BBC had appointed a new correspondent to replace Mr Johnston, who was due to leave Gaza at the end of March, but this would be reviewed.