The previous round, held in Geneva in February, ended without a breakthrough. Soon afterward, the US-Israel war on Iran diverted Washington's attention from Ukraine, and no further discussions were held until the meetings in the Emirates.
Asked at a news conference in Copenhagen about how US officials were handling the negotiations, Zelensky said:"I see changes. I'm very happy with what I hear.".
Zelensky also said humanitarian issues, including exchanges of prisoners of war, were discussed during the talks.
The resumption matters because the war has continued through months without three-way talks, while European governments have warned that decisions about the continent's security could be taken without them.
A central dispute is Ukraine's eastern Donetsk region, most of which is occupied by Russia. The area's so-called fortress belt is treated as vital to Ukraine's defences.
Ahead of the talks, Russian strikes wounded nine people and damaged Ukraine's power network.
Until now, European leaders have largely been excluded from the peace talks. They have pushed to be included amid concern that choices about their continent's security would be made without them.
Some ideas favoured by EU officials, including an unconditional ceasefire as a prerequisite for negotiations, are routinely rejected by Moscow.
An increasingly conciliatory approach toward Moscow has fuelled deep unease in Kyiv and across the European Union. Many in Ukraine are sceptical that the process would produce a fair peace.