Kiev (AFP) - Ukrainian officials on Thursday pledged to investigate after unknown assailants painted Nazi graffiti around a cemetery that holds the remains of Polish officers shot by the Soviet secret police.

The vandals on Wednesday scrawled the name of the SS Galicia division, a Nazi World War II unit that was made up of Ukrainians, in red paint on a monument at the Bykivnia cemetery near Kiev.

The burial ground houses the remains of tens of thousands of people killed by the Soviet authorities under Stalin, including an estimated 2,500 Polish army officers massacred after Moscow signed a pact to split the country with Nazi Germany.

"I can offer assurance that we are taking all measures so that such incidents in Ukraine are investigated as quickly as possible," foreign ministry spokeswoman Mariana Betsa said.

Ukraine and its western neighbour Poland have close ties.

Warsaw was a firm supporter of Kiev after the ouster of a pro-Russian president set off Moscow's annexation in 2014 of Crimea and a Russian-backed insurgency in the east of the country.

But in the past year there has been some renewed rancour over historical disputes, including the war-time killing of Poles by Ukrainian nationalists.

Poland's rightwing-dominated parliament last year stirred Ukrainian anger by recognising as a "genocide" a massacre of 100,000 Poles by Ukrainian nationalists seven decades ago.