Acting Foreign Minister Andriy Deshchytsia tried to persuade protesters not to use violence at the rally on Saturday evening, during which the Russian flag was ripped up, vehicles overturned and stones and eggs thrown at the embassy.
"We must fulfil our international obligations, including defending the right of Russia to have an embassy in Ukraine," he told the protesters, angered by pro-Russian separatists shooting down a military cargo plane in east Ukraine, killing 49 people.
But challenged by the protesters, he added: "Did I say that I am against you protesting I am for you protesting. I am ready to be here with you and say 'Russia, get out of Ukraine'."
"Yes, Putin is a dickhead, yes," he went on to say and the protesters responded by chanting the phrase.
Russian Foreign Minister Sergei Lavrov, in a telephone call with his french counterpart on Sunday, "expressed outrage over the inaction of the Kiev authorities who allowed the rioting outside the Russian embassy," the ministry said in a statement.
Lavrov has protested to the Organization for Security and Cooperation in Europe about the violent rally at the embassy and the United States and the European Union have condemned it.
Alexei Pushkov, head of the Russian lower house of parliament's international affairs committee, said Ukrainian President Petro Poroshenko should dismiss Deshchytsia.
"Poroshenko should change his foreign minister. He doesn't control himself very well," Pushkov said on Twitter, and went on to suggest in televised comments that Moscow should halt all dialogue with Kiev and cut off gas supplies to Ukraine.
Leonid Kalashnikov, Pushkov's deputy on the same committee, told Ekho Moskvy radio station in Moscow that Deshchystia came from the protest movement that toppled Ukraine's previous, Moscow-leaning president and did not know his "craft".
"I can't really imagine how anyone, especially a Russian representative, can sit down at the negotiating table with him after such an outburst," Kalashnikov said.
Ukraine's Foreign Ministry said arrests had been made after the rally, during which windows were smashed and a gate damaged, and that stabilising the situation in Ukraine depended on Moscow's "readiness to stop supporting terrorists" in east Ukraine.
Defending his actions, Deshchytsia told Ekho Moskvy that he had told the demonstrators they could protest peacefully but should not resort to violence.
Asked about his comment on Putin, he said: "I have told you what I want to say. You asked for my comments (on the rally), I've made my comments."