The al Qaeda-linked Abdullah Azzam Brigades had urged Lebanese Sunni Muslims to attack the Iranian-backed Shi'ite militant group Hezbollah a day before Wednesday's suicide bombing in central Beirut.
No claims of responsibility have been made for the attack but the Abdullah Azzam Brigades says it has carried out recent bombings in Lebanon, including an attack on the Iranian embassy in November which killed 23 people, mostly civilians.
The group posted the message on Twitter on Tuesday, before a suicide bomber – said by Lebanese authorities to be a Saudi national – wounded three security officers in a hotel in the capital close to the Saudi Arabian embassy.
Escalating sectarian violence in the region has seen Hezbollah send hundreds of fighters to neighbouring Syria to boost the forces of its ally President Bashar al-Assad against mainly Sunni rebels seeking to topple him.
Gulf states fear Sunnis in Lebanon, Syria and Iraq face oppression at the hands of Iran and its Shia allies in the region.
"The soldiers of the Party of Iran (Hezbollah) and its leaders are beneath you, so gain the approval of Allah by killing and assassinating them!" Sirajuddin Zurayqat, a cleric for the group, said in the audio message.
"You will not have the life of the secure ones until security returns to the people of Syria and Lebanon," he said, according to a translation by the US-based SITE intelligence group, which monitors militant websites.
