Chinese FM Wang Yi calls on both sides to "keep the crisis from spilling over", and Indian FM Subrahmanyam Jaishankar calls for "dialogue and diplomacy" to end the conflict in eastern Europe.
China and India have called at the UN General Assembly for a negotiated end to the Ukraine conflict, while Mali hails the "exemplary and fruitful cooperation" with Moscow.
After a week of pressure at the United Nations General Assembly, Russia's foreign minister on Saturday took the General Assembly rostrum to deliver a fiery rebuke to Western nations for what he termed a "grotesque" campaign against Russians.
Chinese Foreign Minister Wang Yi called on both Russia and Ukraine to "keep the crisis from spilling over" and from affecting developing countries.
"China supports all efforts conducive to the peaceful resolution of the Ukraine crisis. The pressing priority is to facilitate talks for peace," Wang said.
"The fundamental solution is to address the legitimate security concerns of all parties and build a balanced, effective and sustainable security architecture."
During his visit to the United Nations, Wang met with Ukrainian Foreign Minister Dmytro Kuleba, in their first talks since the fighting began.
Earlier this month Putin acknowledged Chinese "concerns" about Ukraine during a meeting with his counterpart Xi Jinping.
India 'on side of peace'
India, unlike China, has a warm relationship with the United States but it has historic ties with Russia, its traditional defence supplier.
"As the Ukraine conflict continues to rage, we are often asked whose side we are on," said India's Foreign Minister Subrahmanyam Jaishankar.
"Our answer, each time, is straight and honest –– India is on the side of peace and will remain firmly there," he said.
"We are on the side that calls for dialogue and diplomacy as the only way out."
Russia enjoyed one rare voice of support on Saturday at the General Assembly. Mali's interim Prime Minister Colonel Abdoulaye Maiga, appointed by coup leaders, hailed the "exemplary and fruitful cooperation" with Moscow.
The junta has welcomed Russia's Wagner Group security firm, despite Western allegations of rights abuses, as France pulled out troops who had been struggling to contain a militant insurgency.