Ban, who is on a visit to Sierra Leone, told a news conference in the capital Freetown he was sending Ivan Simonovic, his assistant secretary general for human rights, to "monitor the human rights situation" in Ukraine.
"What is important and urgent is that the principle of unity, security and the sovereign integrity of Ukraine be protected," he said.
"I urge all parties to lower their temperature and rhetoric and sit down together to have a constructive dialogue to solve the issue."
"Peace and security in Ukraine have regional and global implications so the tension should be defused. I am making this call from Freetown for all sides to sit down and resolve the tension," Ban added.
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Kerry, Steinmeier and Fabius were in Paris on Wednesday for an international meeting on Lebanon, and held informal talks with Russian Foreign Minister Sergei Lavrov on the Crimea, according to a US State Department official.
The UN chief was in Sierra Leone for the closure of the UN Integrated Peacebuilding Office (UNIPSIL), marking the end of 15 years of peace operations during and after its brutal civil war.
"Sierra Leone represents one of the world's most successful cases of post-conflict recovery, peacekeeping and peace-building," he told the news conference, held jointly with the west African nation's President Ernest Bai Koroma.
Between 1991 and 2002, a ruinous conflict raged in Sierra Leone which became known for child soldiers, the sale of "blood diamonds" and widespread rape and murder, with thousands having their limbs hacked off by rebels.