Russia says it has identified three suspects involved in the shooting of high-profile military general Lt Gen Vladimir Alexeyev.
They include the man said to have carried out the attack, who has been named as Russian citizen Lyubomir Korba.
Russia's Investigations Committee (SK) said Korba arrived in the capital, Moscow, in late December "on assignment from Ukrainian intelligence services to commit a terrorist attack". Kyiv has reportedly denied involvement.
Alexeyev, 64, was taken to hospital after the attack in a residential block of flats in the north-western outskirts of Moscow on Friday. He has since regained consciousness after undergoing surgery, according to Russian media reports.
In comments released on Saturday, Zelensky told reporters what had taken place during the second round of US-brokered peace talks in Abu Dhabi, which ended on Friday with no reports of a breakthrough.
Zelensky said "difficult issues remained difficult", including territorial concessions that Ukraine is under pressure to make.
He said the parties discussed, for the first time, the possibility of a trilateral meeting between leaders, not simply representatives, but cautioned "preparatory elements are needed for this".
Asked whether a time frame had been given for an agreement, the Ukrainian leader replied: "The Americans say that they want to do everything by June."
"Why before this summer?" he added. "We understand that their domestic issues in the US will have an impact." These issues include the November midterm elections, which could affect the balance of power in the US government.
As the diplomacy continues, so too are Russian strikes on Ukraine's energy facilities.
"Russian criminals carried out another massive attack on Ukraine's energy facilities," Ukraine's energy minister, Denys Shmyhal, wrote on Telegram.
Substations, which control the flow of electricity, and overhead power lines that "form the backbone of Ukraine's power grid" were targeted, Shmyhal said. Power plants were also struck.
Ukraine's state-owned energy operator, Ukrenergo, said "the power deficit in the power system of Ukraine significantly increased" as a result of the latest attacks.
Shmyhal said neighbouring Poland had been asked for emergency power supplies.
Zelensky wrote on social media that Friday night's attack involved more than 400 drones and 40 missiles. Air-defence systems intercepted most, but not all, of them, the Ukrainian military said.
"The main targets were the energy grid, generation facilities, and distribution substations," he said, adding that damage had been reported in at least four regions.
In the western region of Lviv, the Dobrotvir power plant came under attack, leaving thousands of people without electricity, according to the regional head, Maksym Kozytskyi.
At least 6,000 people were without power as a result of hourly power outage schedules, he added.
