It follows the most significant confrontation between Tehran and Washington in decades, escalating tensions in the region, especially in Iraq, where Gen Suleimani was killed.
"God the almighty has promised to get his revenge … Certainly actions will be taken," he said in an interview with Iranian state television that aired on Monday.
The Quds Forces is a unit of the Islamic Revolutionary Guard Corps and it oversees an array of militant proxies and organises Iran’s operations in the region.
Washington has sanctioned Qanni since 2012 for his work funding the Quds Force operations around the world, including its work with proxies in Iraq, Lebanon and Yemen.
"We promise to continue down martyr Suleimani's path as firmly as before with help of God, and in return for his martyrdom we aim to get rid of America from the region," Qanni said.
Suleimani’s daughter, Zainab, joined Qanni in threatening US military forces stationed in the region while speaking to hundreds of thousands of supporters in Tehran.
“The families of US soldiers in the Middle East will spend their days waiting for the death of their children," she said to the crowd as they cheered.
The killing came amid months of back-and-forth attacks that have put the wider Middle East on edge.
US President Donald Trump vowed on Twitter that Washington will strike back at 52 targets “very fast and very hard" if Tehran took any steps against their troops in the region.
"If Iran attacks an American Base, or any American, we will be sending some of that brand new beautiful equipment their way … and without hesitation!" Trump said on Twitter.
Iran's Supreme leader, Ayatollah Ali Khamenei, along with top officials in Tehran, led prayers in a state funeral for Suleimani on Monday.
Tehran also said it has abandoned the remaining limits of its 2015 nuclear deal with world powers in response to the killing.
Iraq's parliament responded by voting on Sunday to oust US troops from the country.
Trump also threatened to sanctions against Baghdad if US forces were required to leave, Iraq's government would have to pay Washington for the cost of a "very extraordinarily expensive" airbase there.
Source: The National