Obama's announcement effectively eliminates those rules for "international organizations . . . [and] select vetted members of the Syrian opposition, including the Supreme Military Council," Hayden said in a statement Monday.
The order comes as U.S. and Russian officials are working a disarmament deal to force Syrian President Bashar Assad to give up his chemical weapons stockpiles.
Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov agreed to the deal, which would have Assad hand control of those stockpiles to the United Nations.
But serious questions remain on how international regulators will be able to track and contain those weapons stockpiles.
The Pentagon is adamant that any effort to dismantle Syria's chemical weapons stockpile will not involve American troops.
Even if diplomats reach an agreement on destroying the arms, keeping them secure will be a job for Syria's military, Pentagon officials insist.
"No matter what, [Syria] has an obligation" to account for its chemical weapons, Pentagon Press Secretary George Little said Friday.
The regime of Syrian President Bashar Assad "owes this [much] to the international community," Little said.
U.S. military commanders in the Mideast have drafted up a slate of options to address possible security challenges facing Washington and allied efforts to disarm Syria.
Central Command submitted their recommendations to U.S. diplomats before Secretary of State John Kerry's meeting on Saturday with Russian counterparts on taking control of Syria's chemical arsenal, a State Department official said Sunday.
The command's recommendations included "broad parameters . . . to give us some idea of the dimensions of the security challenge" tied to taking control of Syria's chemical stockpiles, Central Command's plans included "nothing very complex" in terms of actual operations to secure the regime's chemical sites, the official said.
The official did not comment as to whether the command's recommendations included plans for U.S. forces to secure those sites.