"This cauldron of tensions is leading more and more countries to take unpredicted decisions with unpredictable consequences and a profound risk of miscalculation," Guterres said in a statement on Monday.
"Geopolitical tensions are at their highest level this century. And this turbulence is escalating," he said with a warning: "We are living in dangerous times."
Guterres, who said that he was in touch with leaders around the world about the situation, had a straightforward message: "Stop escalation. Exercise maximum restraint. Re-start dialogue. Renew international cooperation."
He avoided naming any country in his statement when he spoke of "unpredicted decisions" with "profound risk of miscalculations."
It could apply to the US, which set off the turmoil in the sensitive Gulf and Middle East regions by the attack near the Baghdad airport last week that killed Soleimani, who was the head of the Quds Force of the Iranian Islamic Revolutionary Guards.
And also to Iran, which has threatened retaliation and has announced it would further move along with its nuclear processes that it had stopped in accordance with multi-national deal made in 2015.
US had withdrawn from the deal.
Guterres said, "Even nuclear non-proliferation can no longer be taken for granted."
Militias affiliated with the Quds Force started the current round of confrontation when they attacked a base in Iraq killing a US contractor and President Donald Trump blamed Soleimani for it.
The US State Department said that Secretary of State Mike Pompeo spoke to Guterres and expressed his appreciation for his diplomatic efforts.
The Security Council that met Monday morning could not agree on even a statement on Soleimani's killing or the attack on the United States embassy in Baghdad because of the veto threats from permanent members ranged on either side.
The US mission to the UN said the Security Council's silence on the attack on its Baghdad embassy last week was because permanent members Russia and China would not allow it "to issue the most basic of statements underscoring the inviolability of diplomatic and consular premises."
It said, this "once again calls the Council's credibility into question. Such expressions of support should not be controversial or warrant courage."
Permanent Representatives Zhang Jun of China and Vasily Nebenzi of Russia told reporters that their countries had wanted a more comprehensive statement about all the developments in the region and not just on the embassy attack.
Zhang called the situation "dangerous" in the region and said that Beijing urges the US to not "abuse" the use of force.
Speaking separately, Nebenzia said that Moscow condemned the attack on the US embassy in Baghdad, but it wanted the Council to also deal with the broader issues surrounding it like the violation of territorial integrity of nations and the killing of Soleimani.
Guterres, who painted a gloomy picture of the world at start of a new decade, said, "Everywhere we see many people frustrated and angry. We see increased social unrest and growing extremism, nationalism and radicalization, with a dangerous advance of terrorism in several areas of the world, notably in Africa."
He said that the world faced dangers from "technological conflicts that fracture world markets," widening inequalities and climate change.
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )