MPs in Moscow have moved the date of next year’s presidential election to the anniversary of the annexation of Crimea to try to boost support for Vladimir Putin.
Moscow has warned that the war games will not disrupt international flights.
The treasures, popularly known as Scythian gold, are in the Netherlands because they were borrowed from the four museums in Crimea and one in Kyiv for an exhibition in early 2014 at Amsterdam's Allard Pierson Museum.
"The court ruling is that the artifacts have to be brought back to the state of Ukraine as they form a part of the cultural heritage of the state of Ukraine," Illya Bilderbeek, a spokesman for the Amsterdam district court, said.
Vessels from Russia's Black Sea Fleet have taken up position near the disputed Crimean peninsula - which was illegally annexed from Ukraine in 2014 - to help strengthen the air defences.
The aggressive land grab plunged Ukraine-Russia and east-west relations to their lowest point in years and threatened a new Cold War.
Vladimir Krizhanovsky, a Ukrainian military official, earlier said that the exercises had begun and that everything was going smoothly.