Revolutionary Guards General Mohammad Ali Allahdadi died alongside six fighters from Lebanon's Hezbollah group in the January 18 attack on forces supporting President Bashar al-Assad in Syria's civil war.
Israel has not officially acknowledged carrying out the attack, but was already warned last week of an eventual response.
"We have sent a message to the United States through diplomatic channels telling the Americans that the Zionist regime crossed Iran's red lines by this action," said Deputy Foreign Minister Hossein Amir-Abdollahian.
"In this message, we said those responsible should wait to suffer the consequences of their act," he added, in remarks carried by the official IRNA news agency.
Amir-Abdollahian was speaking on the sidelines of a memorial service for Allahdadi also attended by General Ghassem Souleimani, head of the Guards' elite Quds Force, which is responsible for operations outside Iran.
US State Department spokeswoman Jen Psaki said she would not comment on or confirm what she called "private diplomatic communications" although she did not directly deny that the Iranians had made such a request.
"We absolutely condemn any such threats that come in any form, and we continue to strongly support Israel's safety and security," Mr Psaki told reporters.
She also dismissed any notion that any such message by Iran was made during bilateral talks with the US last week in Switzerland.
"As we've said before, the only issue that is being discussed within the talks concerns Iran's nuclear program. So you can assume that was not a channel in this case," she said.
Mohsen Rezaie, secretary of Iran's Expediency Council, added Hezbollah would eventually retaliate against "this recent atrocity," but that the group was "prudent and has a long term plan and will not be infuriated."
Iran is Assad's main regional ally in his war against the rebels seeking to overthrow him.
Hezbollah's Al-Manar television said the group's six fighters were killed on a reconnaissance mission.
But an Israeli security source said the strike was on "terrorists" who were preparing an attack on the Jewish state.
The incident came days after Hezbollah chief Hassan Nasrallah threatened to retaliate against Israel for its repeated strikes on targets in Syria, and boasted the movement was stronger than ever.
He touted a sophisticated arsenal, including Fateh-110 missiles, which have a range of 200 kilometres or more and are capable of hitting much of Israel.
At least two rockets fired from the Syrian side hit the Israeli side Tuesday, prompting return artillery fire, the Israeli army said.
In 2006, Israel fought a war against Hezbollah that killed more than 1,200 people in Lebanon, mostly civilians, and 160 Israelis, mostly soldiers.
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