Police have arrested the suspected hostage taker, whom the state security service (SBU) identified as 44-year-old Maksym Kryvosh.

Avakov said Kryvosh had served time in prison and the SBU said he had propagated "extremist views".

In a surreal twist to secure the hostages' release, President Volodymyr Zelenskiy said he spoke to Kryvosh by phone and agreed to one of his demands, to promote the 2005 animal rights documentary Earthlings, narrated by Hollywood actor Joaquin Phoenix.

Zelenskiy did so in a six-second clip posted on the presidential Facebook page, which was subsequently deleted.

"I congratulate all those who fought all day for the release of the people in Lutsk and, in fact, for their lives," Zelenskiy said in a statement after the hostages were freed on Tuesday evening.

The SBU published a picture of Kryvosh sprawled on the ground with security personnel standing over him after his arrest. Avakov said an accomplice of Kryvosh was detained in the eastern city of Kharkiv.

Police had blocked off the city centre with armed officers, cars and an armoured personnel carrier while they tried to persuade Kryvosh to free the hostages in a day-long stand-off.

Photos showed a small bus parked in the middle of an empty street, with at least two windows smashed and others covered with curtains. Police said Kryvosh threw a grenade out of the bus; Avakov said Kryvosh had fired shots out of the bus at police.

In posts on social media, Kryvosh had demanded that senior Ukrainian officials publish statements saying that they were terrorists. He also threatened to detonate a bomb in a crowded place.

Zelenskiy said he had spoken to Kryvosh for around 7-10 minutes and persuaded him to release three of the hostages, including a pregnant woman. After that, Zelenskiy agreed to publish the short video clip of him saying, "Everyone should watch" the Earthlings film.

Australian Associated Press