The UN urged restraint after Iranian nuclear scientist Mohsen Fakhrizadeh was assassinated near Tehran on Friday.
While the UN said it condemned extrajudicial killings, it called for all parties to avoid actions that would escalate the situation.
Iranian Supreme Leader Ayatollah Ali Khamenei on Saturday demanded the "definitive punishment" of those behind the killing of a scientist who led Tehran's disbanded military nuclear programme, as Iran blamed Israel for the killing.
Mr Khamenei described Fakhrizadeh as “the country’s prominent and distinguished nuclear and defensive scientist”.
The attack raised the prospect of Iran hitting at the US, Israel's leading ally, as it did this year when an American drone strike killed an Iranian general in Iraq.
The US military said it had moved an aircraft carrier back to the Gulf. An Iranian politician suggested throwing UN nuclear inspectors out in response to the killing.
Syrian Foreign Minister Faisal Mekdad also accused Israel on Saturday as well as "those who supported it", adding that the killing would only make matters worse.
Mr Mekdad was quoted by state media as telling the Iranian envoy in Damascus that Syria was confident Iran would confront what he called the terrorist act on Friday.
Turkey echoed Syria's sentiments and condemned the attack on Saturday, describing it as a heinous assassination and calling for those responsible to be held accountable.
The Turkish Foreign Ministry also urged "all sides to act with common sense and restraint".
Qatari Foreign Minister Mohammed Al Thani also condemned the killing.
On a phone call on Saturday with his Iranian counterpart Mohammad Jawad Zarif, he extended Qatar's condolences to the government and people of Iran and called for self-restraint from Tehran.
Oman, which has acted as a mediator between the US and Iran, sent its condolences.
Foreign Minister Badr Al Busaidi condemned the act, which he said went "against humanitarian and international laws".
Germany on Saturday called on all sides to avoid escalating tensions that could derail any talks on Iran's nuclear programme.
"A few weeks before the new US administration takes office, it is important to preserve the scope for talks with Iran so that the dispute over Iran's nuclear programme can be resolved through negotiations," the Germany Foreign Ministry spokesman said.
Western and Israeli governments have long held the belief that Fakhrizadeh was the architect of a secret Iranian nuclear weapons programme.
