* EU's Oettinger holds out prospects of a sweetened offer
* Hopes to resume three-way talks this month
* Says South Stream project acceptable (Adds quotes, background)
VIENNA, June 16 (Reuters) - The European Union's mediator in a gas standoff between Russia and Ukraine urged Moscow on Monday to consider a compromise gas pricing offer for deliveries to Ukraine and he said he hoped to convene more talks this month.
European Energy Commissioner Guenther Oettinger, who has brokered a series of three-way talks between Russia, Ukraine and the EU, was speaking in Vienna following the latest round of negotiations that ended without a deal in the early hours of Monday.
"My appeal to the Russian partners (is to consider) whether the proposed compromise would not be acceptable for them with some adjustments," he told a news conference.
"Further invitations for trilateral talks in June are foreseen."
Oettinger said gas storage in Ukraine was comfortable at around 12 billion cubic metres (bcm), which should also help to cushion the EU from any knock-on reduction in gas supplies shipped to the EU through Ukraine.
Ukraine's annual gas demand is around 55 bcm so this is equivalent to nearly a quarter of annual demand.
Oettinger said Ukraine intended to fulfil its gas transit commitments to the European Union and he had no doubt that Russia would meet its gas supply pledges to corporate customers in the EU. But he stressed that the EU still needed to top up gas storage.
"If the storage is not filled then perhaps we all will have a problem in winter," he said.
Russian gas exporter Gazprom said early on Monday it was reducing shipments of gas to Ukraine, following the breakdown of talks.
Arguments over the legality of the South Stream pipeline, being built by Gazprom to ship gas directly to Europe while bypassing Ukraine, have complicated the price row.
Oettinger has said the project breaches EU law, but signalled on Monday the issues were not insurmountable.
"South Stream is a project that we indeed accept," he said. (Reporting by Michael Shields and Angelika Gruber; editing by Jason Neely)