Representatives from around 40 countries including China, India, the United States and Ukraine took part in the peace summit, which was held in Jeddah.
"We are very satisfied with the results of the summit," the head of Ukraine's presidential office, Andriy Yermak, said.
"The meeting in Saudi Arabia is a rehearsal for a world in which there is no place for savage aggression (by Russia)."
He said there was an agreement on the next meeting, "but there are no exact dates" and said that "even more countries will participate".
He said a Chinese representative was "present at all events."
"There is no reason to doubt that the principle 'Nothing about Ukraine without Ukraine' is being disrupted," he added.
Russia earlier said that a peace settlement was only possible if Kyiv put down its arms.
Russia, which was not invited to the summit, said that a resolution was possible if Ukraine "stopped the hostilities and terrorist attacks" and if Western countries stopped arms supplies to Kyiv.
It also called on Ukraine to cede its occupied territories to Moscow.
"The original foundations of Ukraine's sovereignty -- its neutral, non-aligned and non-nuclear status -- must be confirmed," foreign ministry spokeswoman Maria Zakharova said in a statement.
Over a year into Moscow's campaign in Ukraine, Kyiv's forces were pressing ahead with their long-awaited offensive to retake occupied territory.
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