President Volodymyr Zelenskyy said Ukraine has proposed a mutual cease-fire on attacks targeting energy infrastructure, while Russia accused Kyiv of striking a key international oil export facility.
"If Russia is ready to stop striking our energy sector, we will be ready to respond in kind," Zelenskyy said in his evening address.
"And this proposal of ours – conveyed through the Americans – has been communicated to the Russian side," he added.
Russia on Monday said that Ukrainian drones attacked the Caspian Pipeline Consortium's Black Sea terminal, which handles 1.5% of global oil supply, damaging the single point mooring (SPM), loading infrastructure and four vast storage tanks.
Separately, the Ukrainian military said it had struck oil loading facilities at the nearby Sheskharis oil terminal in Novorossiysk.
The strikes could be among the most significant on Russia's Black Sea export facilities during the more than four-year-old war with Ukraine, which in the past month has seen Ukraine step up attacks on Russia's energy infrastructure.
Ukraine did not immediately reply to a request for comment about the CPC facilities and Reuters was unable to independently verify the Russian defence ministry statement. CPC declined to comment.
Russia's defense ministry said Ukraine had attacked the CPC's loading facilities with air drones. The CPC's Yuzhnaya Ozereevka terminal exports oil from Kazakhstan and its shareholders include Chevron and Exxon Mobil.
"The Kyiv regime deliberately attacked facilities of the international oil transportation company Caspian Pipeline Consortium in order to inflict maximum economic damage on its largest shareholders - energy companies from the United States and Kazakhstan," the defense ministry said in a statement.
The CPC terminal, located to the south-west of Novorossiysk, handles 80% of Kazakhstan's crude exports.
Ukraine's military said its drones attacked oil loading infrastructure at Sheskharis, about 15 km (9 miles) from the CPC terminal.
As a result of the strike, six of seven oil tanker loading stands were damaged, an official from Ukraine's SBU security agency said, adding that large-scale fires broke out at the sites of the attacks, while the pipeline system's hub and oil metering station were also hit.
Two industry sources had told Reuters that a fire was sparked overnight at the Sheskharis terminal.
According to the sources, the blaze engulfed the main pier of Russia's oil pipeline monopoly Transneft near berths 1, 1a and 2. Berth 1 is able to service tankers with a deadweight of up to 250,000 metric tons, while berth 2 can load tankers of up to 90,000 tons of deadweight, the sources added.
The impact on loading operations was not immediately clear. Transneft did not reply to a request for comment.
Sheskharis typically loads between 600,000 and 700,000 barrels per day of crude oil. Last year it also exported 19.8 million tons of oil products, according to the industry sources.