"The Security Council expresses deep concern regarding the maintenance of peace and security of Ukraine," it reads. "The Security Council recalls that all Member States have undertaken, under the Charter of the United Nations, the obligation to settle their international disputes by peaceful means."
"The Security Council expresses strong support for the efforts of the Secretary-General in the search for a peaceful solution," reads the statement, which also requests U.N. chief Antonio Guterres brief the council again "in due course."
Guterres welcomed the council support on Friday, saying he would "spare no effort to save lives, reduce suffering and find the path of peace."
Guterres met with Russian President Vladimir Putin in Moscow and Ukrainian President Volodymyr Zelenskiy in Kyiv last week.
His visits paved the way for joint United Nations and International Committee of the Red Cross operations that have evacuated some 500 civilians from Ukraine's port city of Mariupol and the besieged Azovstal steel plant in the past week.
The Security Council statement was agreed despite a diplomatic tit-for-tat that has been escalating since Russia launched on 24 February what it calls a "special military operation" and what Guterres blasted as Russia's "absurd war."
Russia vetoed a draft Security Council resolution on 25 February that would have deplored Moscow's invasion. China, the United Arab Emirates and India abstained from the vote. A council resolution needs nine votes in favor and no vetoes by the United States, Russia, China, France or Britain to pass.
The 193-member U.N. General Assembly, where no country has a veto, has since overwhelmingly adopted two resolutions, illustrating Russia's international isolation over Ukraine. Such resolutions are nonbinding, but they carry political weight.
The General Assembly has deplored Russia's "aggression against Ukraine," demanding both that Russian troops stop fighting and withdraw and that there be aid access and civilian protection. It also criticised Russia for creating a "dire" humanitarian situation.