Krug described it as "a concrete and essential involvement", at a conference on Tuesday in Vienna.
The multinational mission to get rid of the weapons is overseen by the UN Security Council and the Organisation for the Prohibition of Chemical Weapons (OPCW). The mission will be fully completed by mid 2015.
Captain Peter Glittenberg, one of two Austrians participating in the mission, said that all chemical weapons that were reported by the Syrian government to the OPCW had been removed from the country and are currently being destroyed on board a US ship, the MV Ray, which has been specially fitted out for the task.
The destruction of Syria’s chemical weapons is vital for Europe’s safety, Klug said. If the weapons were to fall into the wrong hands it would be an "incalculable risk" for Europe’s security, he added.
Syria agreed last September to destroy its entire chemical weapons programme under a deal negotiated with the United States and Russia after hundreds of people were killed in a sarin gas attack in August on the outskirts of the capital, Damascus.
The agreement averted U.S. military strikes in response to the worst chemical weapons attack in decades, which Washington and its European allies blamed on the government of President Bashar al-Assad. Assad blamed the chemical attack on rebels fighting to oust him.
Syria's civil war, now in its fourth year, has killed more than 150,000 people. The United Nations says 10.8 million people need help, while three million others have fled.