Ivan Simonovic also cautioned in an interview with AFP against expecting that Sunday's election would provide a "miracle" that would resolve a crisis that threatens Ukraine's very existence, saying the window of opportunity was closing fast.
The visiting UN assistant secretary-general for human rights said the international community should heed the lessons of the war in the former Yugoslavia to ensure that such a heavy price is not paid in Ukraine.
He said the rebel-held region of Donetsk in the country's eastern coal and steel heartland was running short of crucial supplies such as medicines including insulin.
"I have an impression that Donetsk is on the verge of collapse of social services... the overall system is, I think, on the verge of collapse."
He said that during his discussions with local people in the Donetsk region it was "frightening" how many people were contemplating leaving.
"And if things do not improve, we could have a major wave of displaced persons coming from that area."
Simonovic, a diplomat from Croatia, said he did not believe the situation in Ukraine had yet reached the "point of no return" but warned that could happen if there was an escalation of violence.
'Country increasingly divided'
"That window of opportunity (to end the crisis) may be closing and the opportunity, while is still open, should be used both nationally and internationally."
"Elections will be the beginning of a new phase," he said, just days before the presidential poll being held in the face of Russia's annexation of crimea last month and the uprising in the east.
"But to expect a miracle out of elections is, I think, unrealistic," he added.
"We are facing a country that is increasingly being divided. We are facing a country that may be heading to a very dramatic future scenario. However, we are dealing with a country that can be saved."
Fighting erupted in eastern Ukraine last month after the Ukrainian government launched an offensive against pro-Russian separatists who took up arms against Kiev's rule, seizing over a dozen towns and declaring independence in Donetsk and neighbouring Luhansk.
Simonovic said last week that the death toll in the unrest in the east was close to 130 people as he issued a report warning of an "alarming deterioration" of human rights there.
"This comparison should be done. I think that there must be some lessons learnt," he told AFP, referring to the wars that followed the breakup of the former Yugoslavia with the loss of well over 100,000 lives.
"Such a heavy price should not be paid in Ukraine," he said, calling for greater efforts to prevent a "tragedy".
Simonovic also suggested that the roadmap sponsored by the pan-European security body the OSCE could be improved.
He described the national unity discussions that were launched by Kiev's government last week under OSCE auspices as a "major initiative" but said it was important they were inclusive.
Two rounds of so-called national dialogue have been held but Ukraine has refused to invite the insurgents it considers "terrorists".
Simonovic said the national talks should involve critics of the government who did not take up arms, and were willing to seek "consensus", in a process conducted in parallel with international efforts such as a deal reached in Geneva last month but which failed to make headway on the ground.