Khazali said in a tweet, "The decision of Iraqi Resistance Coordination Commission is not to target the US embassy in the first place."
"It is our right to liberate our country and avenge our martyrs, but we specify the time to respond and it is not far away,” he added.
Kata’ib Hezbollah also said in a statement the rockets attack on the US embassy in Baghdad is an "uncontrolled" act, calling on the government to take the necessary steps to arrest the perpetrators.
"We condemn the indiscriminate attack against the US embassy, as it poses a threat to civilian lives," the group said, calling on "the United States to suspend the military activities in the area for the residents’ safety."
The rockets, which were fired late on Sunday, landed close to the US diplomatic mission, causing sirens blaring within the compound without any casualties apart from some material damage.
Following the attack, the Iraqi military said in a statement that an "outlaw group" had fired rockets at Baghdad's Green Zone, Reuters reported.
The rockets hit a residential complex inside the Green Zone, damaging buildings and cars, but causing no casualties, the statement added.
In a tweet on Sunday night, Iraqi cleric Muqtada al-Sadr also condemned the attack and said he was “ready to cooperate” with the Iraqi government in protecting civilians and diplomatic missions.
"No one has the right to use weapons outside the jurisdiction of the state,” the top cleric said.