KIEV, Ukraine (CNN) -

Militants shot down a Ukrainian military helicopter late Tuesday afternoon in eastern Ukraine, less than a week after Ukraine's president declared a cease-fire in Kiev's fight against pro-Russian separatists, a Ukrainian anti-terror spokesman said.

All nine people who were aboard the Mi-8 helicopter near Slovyansk are believed to have died, said Vladislav Seleznev, spokesman for Ukraine's anti-terror operation.

A missile fired from a man-portable air-defense system hit the helicopter, Seleznev said. Afterward, the militants who brought down the aircraft hid in a nearby village, Bylbasovka, according to Seleznev.

Russia and Ukraine have been engaged in a tense standoff since March when Russia annexed the previously Ukrainian peninsula of Crimea and massed troops along other parts of its border with Ukraine.

Ukraine's government in Kiev has accused Russia of allowing weapons and military equipment to cross the border illegally into the hands of pro-Russia separatists, who have led uprisings in Ukraine's eastern Donetsk and Luhansk regions.

Ukrainian President Petro Poroshenko on Friday declared a cease-fire with pro-Russia separatists, saying military units would respond only if they're attacked. He warned militants to abandon their weapons before the cease-fire expires on June 27.

The cease-fire includes the closure of the Ukraine-Russia border, and Poroshenko called for changes to Ukraine's Constitution to decentralize power.

Russian President Vladimir Putin last week welcomed the cease-fire and said it "should be used to begin constructive negotiations and political compromises between the opponent parties in eastern Ukraine," according to the Kremlin.

On Tuesday, Putin asked Russia's upper house of Parliament to cancel a March 1 resolution that authorizes Russia to use force in Ukraine, state-run news agency ITAR-Tass reported. Lawmakers had passed that resolution weeks before Russia annexed Crimea.

Russia's annexation of Crimea and the pro-Russian uprising in eastern Ukraine came after Ukraine's Parliament ousted Viktor Yanukovych from the presidency on Feb. 22.

Yanukovych's departure came after months of protests in Kiev -- demonstrations motivated in part by his decision to back out of a trade deal with the European Union in favor of closer ties with Russia.