ATHENS, May 20 (Reuters) - Greek Prime Minister Kyriakos Mitsotakis has urged the European Union to bring down prices as soon as possible, which he labelled a crucial political challenge ahead of European parliamentary elections.

Anger at falling living standards is shared by millions of Europeans and is expected to dent support for mainstream parties in the June 6-9 vote for the 720 lawmakers of the EU assembly.

In a May 18 letter to European Commission President Ursula von der Leyen, the Greek conservative leader said that inflation had highlighted problems in the functioning of the markets which led to discrepancies in prices of essential goods across the 27-nation bloc.

In Greece, he said, and other countries including Belgium, Croatia, the Czech Republic, Denmark and Slovakia, essential consumer goods made by multinational companies were sold at "unreasonably high prices" compared with other EU member states.

He added that one of the main reasons was that multinationals had imposed territorial supply constraints (TSCs) on EU member states' markets to take advantage of their dominant position.

The EU needed to demonstrate that it could "intervene decisively, swiftly and effectively" to solve such problems.

"The recent inflation crisis has led to a significant erosion of the purchasing power of European citizens and has highlighted on the one hand the asymmetric power of some large multinational companies ... and on the other the untapped collective power of our Union," Mitsotakis said.

The cost-of-living crisis was triggered by a global surge in inflation exacerbated by energy price spikes brought on by the Ukraine war. Greece had the second lowest level of GDP per capita in the EU in 2023, according to Eurostat data.

Mitsotakis proposed stopping multinational companies selling identical consumer products under different brands in different EU member states and the strengthening of EU competition laws.

He also said that unfair commercial practices in supplier-retailer relations should be prohibited, and that language restrictions on the labelling of essential consumer goods should be removed. (Reporting by Renee Maltezou; Editing by Nick Macfie)