The group on Friday demanded at a news conference in Beirut the resignation of President Emile Lahud and the dismissal of all security officials in Lebanon, in the wake of the assassination of former Prime Minister Rafiq al-Hariri.
The Islamic Group added that it wanted Lahud to resign only after parliamentary elections and the restoration of stability.
For his part, Lahud cautioned that the country's political crisis could affect economic institutions.
At a meeting with top executives of major Lebanese economic institutions, Lahud reiterated his call for dialogue with the opposition, which he accused of exploiting foreign pressure.
Chain of events
Al-Hariri was killed on 14 February along with 14 others in a blast that targeted his convoy in the heart of Beirut.
The assassination has provoked mass demonstrations in Lebanon against Syrian dominance of the country.
The government of Lebanon is investigating the murder but has rejected US and French demands for an international inquiry. However, it has said it will assist a UN team of investigators who began working on the case on Friday in Beirut.
Lebanese opposition figures have accused their government and Syria of involvement in the assassination. The two governments have strongly denied the charge.