THE HAGUE, Netherlands — The United Nations’ highest court on Wednesday rejected nuclear disarmament cases filed by the tiny Pacific nation of the Marshall Islands against Britain, India and Pakistan, saying it did not have jurisdiction.

In a blow to disarmament activists, the International Court of Justice ruled that the Marshall Islands failed to prove that a legal dispute over disarmament existed between it and the three nuclear powers before the case was filed in 2014, and that “consequently the court lacks jurisdiction.”

It took a casting vote by the court’s President Ronny Abraham to break an eight-eight deadlock between the court’s 16 judges on the question of jurisdiction in the case against Britain.

In the cases against India and Pakistan, the margin was nive-seven.

Phon van den Biesen, a Dutch lawyer who represented the Marshall Islands, said he was deeply disappointed by the rulings.