Johnston, who was abducted on 12 March, is the only Western correspondent based full-time in the Gaza Strip.
The journalist turned 45 while in captivity in May.
Journalists working in the BBC and other newsrooms across the world paused for one minute yesterday at 1315 GMT to show their support.
In Scotland, Mr Johnston's parents released 100 balloons to mark the days passed since his abduction.
Director of BBC News Helen Boaden said: "On the 100th day we are more steadfast in our support for Alan than ever and our thoughts are always with his family."
The militant group Army of Islam has said it kidnapped Johnston and has demanded that Britain free Muslim prisoners, particularly the Islamist cleric Abu Qatada.
The group issued a video of him on 1 June in which he said he was being treated well and criticised the British military presence alongside the United States in Afghanistan and Iraq.
Britain's National Union of Journalists urged fellow reporters to "spare a thought for Alan".
Last month, the Archbishop of York made an appeal for the release of Johnston in which he told of his own captivity under the regime of Idi Amin in Uganda.
Dr John Sentamu shared his experiences with an audience of national editors and broadcasters at the annual London Press Club Awards, describing how "the temptation to give up hope of release was always present".
"But my faith in Christ, my knowledge of the prayers being said on my behalf, these two things were instrumental in being able to survive each day in captivity," he said.
He urged the faith community to pray for journalists like Johnston.
"Journalists, whether imprisoned or not, deserve the supportive prayers of the faith communities and the critical solidarity of all lovers of freedom. It is also true to say that those people persecuted for their religious faith deserve the attention of journalists," he said.
