Ukrainian president Petro Poroshenko says he believes the conflict with Russian-backed separatists in the east is on the wane and that peace efforts will work.
In a news conference outlining his plans for Ukraine over the next half-decade, Mr Poroshenko said: "I have no doubt whatsoever that my peace plan will work and that the main and most dangerous part of the war is behind."
His proposals were a foundation for agreements this month aimed at ending the conflict that has killed at least 3,500 people since mid-April.
The first step was a ceasefire called three weeks ago that in the beginning was repeatedly violated. But in recent days, reports of breaches have decreased.
Mr Poroshenko was speaking the day after prime minister Arseniy Yatsenyuk urged the United Nations not to lift sanctions against Moscow until his country regains control over its entire territory, including Crimea.
Ending a day of intense discussions over the growing global threat of extremist groups, Mr Yatsenyuk told the UN General Assembly of world leaders that "we know what terrorism means".
He demanded that Russia pull back its forces from eastern Ukraine, "stop the supply of Russian-led terrorists" and start "real talks, peace talks".
The months-long fighting between pro-Russian separatists and Ukrainian forces has been another major theme of speeches at the global assembly this week.
Mr Yatsenyuk's comments on sanctions revealed concerns about president Barack Obama's earlier address to the world meeting.
If Moscow follows through on a ceasefire signed this month with Ukraine, the US will lift economic sanctions that have damaged Russia's economy, Mr Obama said. He said the agreement "offers an opening" for peace.
The US has imposed multiple rounds of economic sanctions targeting Russia's energy, defence and financial sectors, as well as penalties on government officials and other individuals close to Russian president Vladimir Putin. The European Union has also ordered sanctions.
So far, however, the sanctions have done little to shift Mr Putin's approach to the crisis.
Mr Poroshenko said he is working to arrange a meeting in the next few weeks with Mr Putin and that he believes there has been a "transformation" of Moscow's aims regarding Ukraine.
Russia at first wanted to tear Ukraine apart, he said, but now "the relationship with Russia and the plans of Russia are changing".