VENICE—Kevin Costner says the poor box-office performance of his Western epic “Horizon: An American Saga” probably led the studios to delay the release of its sequel, but he refused to be downhearted.

Putting a positive spin on the setback, Costner said the decision meant that he could premiere “Chapter 2” at the Venice Film Festival, just four months after the first installment opened to poor reviews at the Cannes Film Festival.

“It didn’t have overwhelming success,” the US actor-director Costner told reporters on Saturday.