The guard's website quoted Gen. Hossein Salami as saying, "Mr. Trump! Our revenge for martyrdom of our great general is obvious, serious and real."
President Trump warned this week that Washington would harshly respond to any Iranian attempts to take revenge for the death of Gen. Qassem Soleimani, tweeting that "if they hit us in any way, any form, written instructions already done we're going to hit them 1000 times harder."
The president's warning came in response to a report that Iran was plotting to assassinate the U.S. ambassador to South Africa in retaliation for Soleimani's killing at Baghdad's airport on January 3.
"We took out the world's number one terrorist and the mass murderer of American troops and many, many troops and many people all over the world," Trump said. "Qasem Soleimani is dead. He's dead. Bad guy. Bad guy. Very bad guy."
Salami had denied the report of an Iranian plot to assassinate Ambassador Lana Marks but made clear that Iran intends to avenge the general's death.
"Do you think we hit a female ambassador in return to our martyred brother?' the general said. "We will hit those who had direct and indirect roles. You should know that everybody who had role in the event will be hit, and this is a serious message. We do prove everything in practice."
In January, Iran launched a ballistic missile attack targeting U.S. soldiers in Iraq in response to the fatal drone strike.
Tensions between Tehran and Washington have been at their highest levels in decades ever since Trump in May 2018 pulled the United States out of Iran's nuclear deal with world powers and ramped up economic sanctions.
Tehran has continued to expand its stockpile of enriched uranium and pressured other nations to offset the harm of U.S.-imposed sanctions, while insisting it does not want to develop a nuclear weapon.
The Associated Press contributed to this report.