The political head of Palestinian militant group Hamas was killed early on Wednesday in Tehran, where he was attending the inauguration of Iran's President Masoud Pezeshkian.
Iran and the Hamas militants, which Tehran supports, vowed to retaliate and blamed the strike on Israel, which has declined to comment.
ISNA news agency said Safadi "met and held consultations with" acting foreign minister Ali Bagheri after landing in Tehran for a rare visit.
Earlier the official news agency IRNA said that Safadi would "exchange views with Iranian officials on regional and international issues" during his visit to Tehran, and would be meeting Bagheri.
The Jordanian foreign ministry said Safadi would deliver a message from King Abdullah II to the Iranian president on "the situation in the region and bilateral relations".
The royal court in Amman meanwhile said that King Abdullah had received a phone call from French President Emmanuel Macron "which covered the dangerous situation in the region".
The king appealed "further international efforts to reach comprehensive calm and prevent a regional expansion of the conflict", a statement said.
Iran has held talks with multiple Arab countries including Jordan, Egypt, Oman and Qatar among others since Haniyeh's killing.
Tehran repeatedly reaffirmed its "inherent right" to take action against Israel.
Israeli Prime Minister Benjamin Netanyahu says his country is at "a very high level" of preparedness for any scenario -- "defensive and offensive".
Haniyeh's killing came hours after Israel killed a senior commander of the Lebanese Tehran-backed Hezbollah militant group, Fuad Shukr, which Israel blamed for a deadly weekend rocket strike on the Israeli-annexed Golan Heights.
Iran's Revolutionary Guards have said Haniyeh was killed by a "short-range projectile" launched from outside his accommodation in northern Tehran.
Israeli military spokesman Daniel Hagari had earlier told journalists "there was no other Israeli aerial attack... in all the Middle East" on the night Shukr was killed in Lebanon.
The dual killings are the latest of several major incidents that have inflamed regional tensions during the Gaza war, which has drawn in Iran-backed militant groups in Syria, Lebanon, Iraq and Yemen.
