A high-ranking foreign ministry official who is heading the delegation said the assassination was "most certainly" linked to his visit.
He sought to play down his role in efforts to avert a major battle between the US military and Sadr's Mehdi Army militia, although it was unclear if the apparent change of position was a result of the killing.
Meanwhile three Japanese hostages were released on Thursday.
An AFP correspondent saw the body of first secretary Khalil Naimi lying in his bullet-riddled car on a Baghdad street after his murder.
Two bullets had pierced the windshield and eight bullet holes were visible on the driver's door.
Iranian foreign ministry official Hossein Sadeghi, responsible for Gulf affairs, described the murder as "savage" and said there was a clear link between the assassination and his delegation's visit.
"Such savage moves are condemned and deplored by the Islamic Republic of Iran," he said.
It was not immediately clear whether the assassination had had any direct impact on Sadeghi's plans in Iraq, although the envoy ruled out holding any talks with Sadr after earlier hinting that this might be possible.
"This visit definitely is not designed to mediate any standoff or any confrontation. The purpose of it is assessing the general situation in Iraq," he said.
"The whole objective is to hear everybody's views at this stage."
The envoy's comments appeared to contradict those of Foreign Minister Kamal Kharazi who had said on Wednesday that the delegation was in Iraq to "help in improving the situation ... and solving the crisis."
Kharazi said the team had been sent at the request of arch-foe the United States, although Washington insisted that the proposal was a British one, which it had not opposed.
Inside Iraq on Thursday, coalition officials sought to play down Iran's role.
"We are not involved in any discussions with the Iranians regarding Sadr," said senior civilian spokesman Dan Senor. The crisis over Sadr "has to be solved by Iraqis, not Iranians."
The chairman of the US Joint Chiefs of Staff, General Richard Myers, went further on an unannounced visit to Baghdad, saying the last thing Iraq needed was "influence from neighbouring countries trying to promote or protect their own self interest."
Washington has sent thousands of armoured infantry to the region around the holy city of Najaf, where Sadr took refuge following an uprising by his militia forces last week.
Sadr unleashed his militiamen at the beginning of April, seizing control of towns in central and southern Iraq after one of his associates was arrested and one of his newspapers was shut down for allegedly inciting anti-US violence.
His uprising also came after a warrant was issued for his arrest in connection with the murder of a rival cleric last year.
On the ground in Najaf, all was quiet on Thursday. Iraqi police were seen around the city's main streets, while Sadr's black-clad fighters milled around the mausoleum of Hazrat Ali (RA).
Sadr said on Thursday he was prepared to meet the Iranian delegation in Najaf, but aides to the cleric said the contents of any Iranian proposal remained unknown.
An aide to the radical cleric, Hazem al-Araji, told AFP that although Sadr was open to mediation, he would not abandon his main demands - the release of detained supporters and guarantees that US troops would not enter the holy cities of Karbala, Najaf and Kufa.
"Sayyed Moqtada is prepared to do whatever Iraq's Shia leadership tell him to do as long as it is in the interest of Iraq and the Iraqi people," said Araji, who was himself briefly detained by US troops on Tuesday.
Another aide said on Wednesday that the cleric was willing to disarm his Mehdi Army and appear before a court under a future "legitimate and democratic" Iraqi government.
But Araji sought to downplay those offers, raising doubts over the cleric's true position amid a barrage of statements and counter-statements.
What is clear is that Sadr has significantly toned down his rhetoric over the past week as US troops massed near Najaf with the stated mission of killing or capturing him.
Only last Friday Sadr was calling on all Iraqis to join his uprising to drive the US-led coalition out, warning of a mass Shia uprising.
Al-Jazeera television showed Japanese hostages - aid workers Noriaki Imai, 18, and Nahoko Takato, 34, as well as photojournalist Soichiro Koriyama, 32 - chatting and sharing juice with Iraqi clerics who had helped secure their release.
"The three have been released," Sheikh Abdul Salam Kubaissi said, confirming that they were at the headquarters of the Committee of Muslim Scholars at the Umm al-Qura mosque in west Baghdad.
"They are in very good health," he said, adding that they had been handed over to the Japanese embassy, while other Japanese officials in Amman said the trio would be flown home through Dubai.
US military officials said for the first time that Al-Qaeda might be one of many groups involved in the spate of kidnappings in Iraq.
Defence Secretary Donald Rumsfeld, while insisting that the bloody insurgency in the volatile town of Fallujah had been contained, said on Thursday some 20,000 US troops due to rotate home will stay longer in Iraq.
"Essentially we've approved the extension of roughly 20,000 forces, people who are currently in the theater," Rumsfeld told a Pentagon press conference in Washington, adding that about one quarter of those would be National Guard and National Reserve troops.
General John Abizaid, commander of US forces in Iraq, requested "additional combat capability for the period ahead," Rumsfeld said.
"I've approved General Abizaid's request," he said.