SCHLOSS ELMAU, Germany, June 25 (Reuters) - Leaders of the Group of Seven rich democracies are having "very constructive" discussions on a possible cap on Russian oil imports, a German government official said on Saturday shortly before the start of the annual three-day G7 summit.

The proposal is part of broader G7 discussions on how to further crank up the pressure on the Kremlin over its invasion of Ukraine without stoking global inflationary pressures.

The Ukraine war, energy and food shortages and the darkening global economic outlook are expected to dominate the agenda of the summit that is taking place this year in Schloss Elmau, an alpine castle resort in southern Germany.

The United States, Canada and Britain have already banned imports of Russian oil while European Union leaders have agreed an embargo that will take full effect by end-2022 as part of sanctions on the Kremlin over its invasion of Ukraine.

With energy prices soaring though, the West fears such embargoes will not actually put a dent in Russia's war chest as the country earns more from exports even as volumes fall.

A price cap could solve that dilemma, while also avoiding further restricting oil supply and fueling inflation, officials say, but for it to work, it requires buy-in from heavy importers like India and China.

"We are on a good path to reach an agreement," the official said.

The official said the G7 was also discussing the need to combine ambitious climate goals with the need for some countries to explore new gas fields as Europe rushed to wean itself off Russian gas imports. (Reporting by Sarah Marsh and Andreas Rinke; Editing by Sandra Maler)