Carter called for NATO nations to stand united against an aggressive Russia but insists US is not seeking a conflict with Moscow.
Pope Francis encouraged Russian President Vladimir Putin to engage in “sincere” international efforts aimed at bringing peace to Ukraine as the two men met privately at the Vatican on Wednesday.
Russia last year offered few resolutions for cease-fire, but they were unpopular with council members angry over its annexation of Crimea.
Russia circulated a draft resolution in the UNSC endorsing the agreement and calling on all parties involved to carry it out.
German Chancellor Angela Merkel and French President Hollande are set to hold talks with Russian President Putin.
The flurry of high-level diplomacy aimed to end the fighting in eastern Ukraine that is threatening European security.
US President has opposed the idea of sending weapons to Ukraine but this position could change in the light of recent events.
The shelling damaged a hospital, six schools and five kindergarten schools.
Government forces have been fighting Russia-backed separatists in eastern Ukraine for 10 months in a conflict
The Security Council is due to discuss the worsening crisis in Ukraine at a meeting on Wednesday, requested by Lithuania.
German minister called for drawing a division line between the government troops and pro-Russian rebels in Ukraine.
But Putin attended the annual forum’s wrap-up lunch and praised the “constructive” discussions.
Russian President Vladimir Putin intends to cut short his attendance at G20 summit in Australia.
US told UNSC there needs to be greater international pressure on Russia to abide by a ceasefire in Ukraine.
The UNSC is holding its 26th emergency session on Ukraine amid worries about a renewal of full-scale conflict.