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Mohamed Abushahab, the UAE's Deputy Permanent Representative to the UN, said “we deplore the ongoing violence in Ukraine".
He stressed the need “for restraint, a ceasefire, and a peaceful resolution of the conflict” in a statement.
On Tuesday, the Emirates will accept the rotating presidency of the 15-member Security Council, with Ambassador to the UN Lana Nusseibeh taking the chair.
The handover comes on the sixth day since Russian troops crossed the Ukrainian border and amid growing Ukrainian civilian casualties.
Reports and video footage showed Russian missiles striking residential districts of Ukraine's second city, Kharkiv, which has a population of 1.6 million, on Monday. Ukraine's government said dozens of civilians died.
“The humanitarian situation in Ukraine has deteriorated significantly in recent days, as the continued fighting results in damages to civilian infrastructure and civilian casualties and deaths,” Ambassador Abushahab said.
“All civilians who are trying to find a safe place must be allowed to do so unhindered, without being subjected to discrimination.”
He added: “The continuation of the fighting will lead to further losses among civilians, in addition to worsening the humanitarian situation, which is exacerbated by the extreme temperatures this winter, as civilians are fleeing the crisis, seeking refuge and safe havens.
“Therefore, we urge all parties to implement their obligations under international law, including by allowing humanitarian aid to reach those in need and to refrain from targeting civilians.
“In conclusion, my country reiterates the importance of working to reach an immediate ceasefire and seeking peaceful solutions that serve regional and international security and stability.”
The UAE, one of 10 temporary council members serving two-year terms, will hold the presidency for one month.
Ms Nusseibeh is expected to set out her country's policies and focus in a session in New York later.
On Monday night, the Security Council ratcheted up sanctions on Yemen's rebel Houthi group following missile and drone strikes on the UAE and Saudi Arabia this year.
The new sanctions, proposed by the Emirates, expand a UN arms embargo against several Houthi leaders to include the whole group.
The Houthi militias were formally labelled a “terrorist group” in the resolution, which 11 of the 15 council members backed.