Mohsen Rezaei added that Israel had a role in the assassination of Soleimani and informed the United States about the commander's flight from Damascus to Baghdad.
The Expediency Council advises Supreme Leader Ayatollah Ali Khamenei on policy matters and makes decisions on legislative issues between the Iranian Parliament and the Guardian Council.
Rezaei made almost identical comments in January, saying "If [US President Donald] Trump retaliates to Iran’s revenge, we will strike Haifa, Tel Aviv and wipe out Israel," adding that Iran is "very serious" about taking revenge and would target all US interests in the region.
On Saturday, Rezaei stressed to Al Mayadeen that Iran's goal is currently to "get the United States out of the region."
"We entered a new front against America because America started confronting us publicly and formally," said the Iranian official, adding that all US bases and aircraft carriers in region are under Iranian surveillance.
"Even when American soldiers go to hotels in Kuwait and Bahrain, we monitor them," said Rezaei.
Soleimani and Iraqi militia commander Abu Mahdi al-Muhandis, along with at least 10 other people, were killed in a US air strike in Baghdad on Thursday.