The International Committee of the Red Cross said three volunteers with the Syrian Arab Red Crescent were wounded, one seriously, when their ambulance was fired upon after it ran over downed power lines.
"The Syrian Arab Red Crescent, the International Committee of the Red Cross and the International Federation of Red Cross and Red Crescent Societies join in calling on all those involved in the violence to do their utmost to facilitate Red Crescent efforts to come to the aid, in a fully impartial manner, of those in need," the ICRC said in a statement.
The ICRC said circumstances surrounding the shootings were unclear.
Syria lost one of its remaining supporters when Iranian President Mahmoud Ahmadinejad told a Portuguese television station that responding to unrest with military force wasn't appropriate.
Damascus has faced increasing international isolation for its violent crackdown on anti-regime demonstrators. More than 2,000 people have been killed, allegedly by Syrian forces, since the uprising against Syrian President Bashar Assad began early this year.
ICRC President Jakob Kellenberger met with Assad this week following a visit to the central prison in Damascus.
Kellenberger in a statement said Syrian authorities granted the ICRC access to detainees held by the Interior Ministry but hoped to gain access to all prisoners.