The al-Hayat newspaper reported that al-Qaeda issued the statement from the Palestinian refugee camp of Nahr el-Bared in northern Lebanon.
"The organization has arrived in Lebanon and we will work on destroying this corrupt government that receives orders from the American administration," al-Hayat said, quoting the statement.
Although it was impossible to verify the authenticity of the message, Information Minister Ghazi Aridi cast doubt on its veracity Monday.
"There is nothing that proves that this statement was issued by al-Qaeda," he told reporters Monday following a cabinet meeting in which the government approved a UN draft setting up an international tribunal to try suspects in the 2005 assassination of former Prime Minister Rafik Hariri.
Sympathizers in Palestinian refugee camps
Aridi suggested the statement could be the work of local or regional groups that were opposed to the international tribunal in an attempt to intimidate the ministers ahead of the vote on Monday.
Al-Hayat did not say how it obtained the message, and Palestinian factions denied any such statement was issued from the camp. Following a meeting by representatives of various Palestinian factions in Nahr el-Bared camp, they issued a statement saying there was "absolutely no presence" for al-Qaeda in Palestinian camps in northern Lebanon.
Although al-Qaeda has rarely carried out attacks in Lebanon, it is believed to have sympathizers among extremist factions in Palestinian refugee camps.
Lebanon's Interior Minister Ahmed Fatfat has warned in recent months that al-Qaeda was attempting to establish itself in Lebanon.
In December, al-Qaeda in Iraq claimed responsibility for a rocket attack into northern Israel apparently carried out by a radical Palestinian group, and Fatfat has said Lebanese authorities had broken up four al-Qaeda cells this year.