Rouhani also said Iran would retaliate over Mohsen Fakhrizadeh's killing at a time of its choosing. An Israeli cabinet minister said he had "no clue" who was behind the ambush by gunmen on Fakhrizadeh's car, the BBC reported on Saturday.
Israel has previously accused the physicist of being key to a covert nuclear weapons programme.
Fakhrizadeh was Iran's most renowned nuclear scientist, who headed the ministry of defence's research and innovation organisation.
His killing threatens to escalate tensions over Iran's nuclear programme with the US and its close ally Israel.
President Rouhani said on Saturday his country would respond "in due course" but that Fakhrizadeh's killing would not push Iran into making hasty decisions.
"Iran's enemies should know that the people of Iran and officials are braver than to leave this criminal act unanswered," he said in a televised cabinet meeting.
"In due time, they will answer for this crime," he added.
In an earlier statement, the president accused the "the mercenaries of the oppressive Zionist regime" - referring to Israel - of being behind the attack.
"The assassination of martyr Fakhrizadeh shows our enemies' despair and the depth of their hatred... His martyrdom will not slow down our achievements."
Iran Supreme Leader Ayatollah Ali Khamenei also called for the "punishing" of the perpetrators of the attack "and those who commanded it", in a tweet on Saturday.
His military adviser, Hossein Dehghan, had earlier vowed to "strike" the attackers like thunder.
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