The US ambassador to the United Nations in Geneva said on Tuesday it was "a travesty" that Syria would head the CD, leaving briefly when the Syrian representative took the floor.
The CD chair rotates alphabetically every four weeks and Syria's turn came round on Monday, although the conference will meet in full session only from Tuesday.
"It is shameful that a regime that continues to use chemical weapons to murder its own people has the audacity to accept the presidency of the very organization that established the Chemical Weapons Convention", U.S. Ambassador to the U.N. Nikki Haley said in a statement.
During the first open CD session of Syria's presidency on Tuesday, the United States led a number of diplomats in protest.
"Syria's presence here's a travesty".
Addressing members of the conference on Tuesday, Syrian Ambassador Hussam Edin Aala scolded the US for its complaints and spent the majority of his remarks on nuclear - not chemical weapons - disarmament and begrudging nuclear states for failing to continue talks on nuclear arms control.
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The storm surrounding family separations by immigration authorities has been brewing for several months. He has incorrectly blamed the Democrats for the practice, saying: "We have to break up families".
Wood walked out as Syria's envoy made opening remarks, but later returned.
Guterres said that he hopes Syria's involvement in the conference will not have a "negative impact" on the conference's disarmament efforts, but simultaneously called for "steps to end and prevent the use of other weapons of mass destruction, especially chemical weapons".
"But we will fundamentally alter the nature of our presence in the plenaries", he said, before moving in protest to a seat usually reserved for assistants.
Wood stressed that the U.S. would not "permit "business as usual" in the CD while Syria presides over this body".
The French representative also said Syria "does not have the moral authority to lead this body".
The 65-nation conference is the world's most important disarmament negotiating forum, though it has achieved little in recent years.