Van Rompuy, who expressed his "sincere condolences" over the tragic incident, said the declaration by Lavrov and Ashton had his full support on behalf of the 27-member bloc.
He also condemned the use of violence and called for a "full, immediate and impartial" inquiry into the incident as well as the "immediate opening of crossings" to and from Gaza.
Bangladesh's Ministry of Foreign Affairs said in a statement on Tuesday that Bangladesh is "shocked and saddened at the unwarranted attack on unarmed civilians" onboard the ships and the loss of life.
The Bangladeshi government also called for collective international action to end the siege immediately, and to allow the Palestinians to return to normal life.
A group of Syrian journalists and artists denounced on Tuesday the Israeli attack, calling on the international community to take responsibility by putting an end to the Israeli acts.
Dozens of Syrian journalists, writers and artists gathered at the Journalists Union in Damascus, bearing signs and banners with protest words such as "Israel is the center of terrorism in the region" and "Salute from the heart to the Freedom Fleet martyrs."
Nearly 1,000 Australians also protested in Sydney on Tuesday in condemnation of the attack on humanitarian aid deaths.
