BRUSSELS—The Dutch prime minister Mark Rutte said Thursday that he was pessimistic a solution could be found which allows the Netherlands to ratify an EU pact with Ukraine, raising fresh doubts about a key symbol of support for the country’s pro-Western government.

Mr. Rutte said he told EU leaders, gathered at a summit in Brussels, that no solution was in sight which would allow him to win political backing in the Dutch parliament to ratify the pact.

“I...