Johnston spoke of the suffering that Gazans have endured and urged the lifting of sanctions imposed to pressure the Hamas-led Palestinian government into recognising Israel's right to exist.
He criticised the British military presence alongside the US in Afghanistan and Iraq, saying: "In all this, you can see the British government is endlessly working to occupy Muslim lands against the will of the people in those places."
The group repeated its demand on the video for Britain to free Muslim prisoners, particularly Abu Qatada, a London-based Palestinian-Jordanian, who faces deportation from the UK.
|"In all this, you can see the British government is endlessly working to occupy Muslim lands against the will of the people in those places"|
Alan Johnston, BBC Gaza correspondent
In London, a spokesman for the British foreign office said: "We are urgently trying to check out the reports."
Abu Qatada, who is suspected of links to al-Qaeda, has been described by the British government as a "significant international terrorist".
He is one of more than a dozen Arab men whom Britain has been holding under detention or house arrest as threats to national security, while acknowledging that it does not have sufficient evidence to put them on trial.
The recording was posted on the al-Ekhlaas website often used by armed groups, and was accompanied by what appeared to be a picture of Johnston's BBC staff card.
Last week, an aide to Ismail Haniya, the Palestinian prime minister, said
Johnston was alive and well, and could soon be released.
He has been missing longer than any Western journalist kidnapped in
Gaza, and his disappearance has touched off numerous protests and solidarity marches in London and the Palestinian territories.
The British government has previously said it would not make deals to secure the journalist's release.