Events have taken place in London and Gaza to mark two weeks since BBC reporter Alan Johnston went missing.
Thompson and the BBC's Simon Wilson in Gaza led proceedings
The BBC set up a satellite link between Gaza and Television Centre so staff and supporters could exchange messages of support on giant screens.
Director General Mark Thompson praised Mr Johnston's commitment for reporting from Gaza in very difficult conditions.
"All of us in London and in Gaza want him home," Mr Thompson told about 100 journalists and members of staff.
Mr Thompson described Alan Johnston as "one of those amazing BBC people who make extraordinary sacrifices and take considerable risks because they believe a story needs to be told".
"He remained with his friends and colleagues in Gaza when others left, and as you have heard, Alan has many friends and colleagues in Gaza."
"We continue to talk to people in the Middle East and in the UK to try to secure Alan's release," he added.
Speaking for the Palestinian journalists' syndicate in Gaza, Shadi al-Kashif made a pledge directly to the missing journalist that their protests "will not stop until your release".
Palestinian officials have said all possible efforts are being made to secure Mr Johnston's release.
Gaza has already seen numerous demonstrations in support of the missing BBC correspondent.
On Sunday more than 100 journalists, politicians, and others attended a rally in Gaza calling for his release and last Wednesday Palestinian journalists began a rolling strike.
There have also been numerous international demands for his immediate release, including from the Arab League, the UK government and the EU.
Mr Johnston has been the BBC's correspondent in the Gaza Strip for the past three years - and the only foreign journalist from a major media organisation based in Gaza.
The BBC describes him as a highly experienced and respected reporter.
Aged 44, he was born in Tanzania and educated in Scotland.
He joined the BBC World Service in 1991 and has spent eight of the last 16 years as a correspondent, including periods in Uzbekistan and Afghanistan.