Speaking in Moscow, Russian President Vladimir Putin said Russia was offering the discount as a "partnership deal."
Russia's energy minister, Alexander Novak, specified the price offered as $385 per 1,000 cubic meters of gas.
"We believe that our offer is more than in a partnership spirit, aimed to support the Ukrainian economy at a rather difficult time," Putin said in televised remarks.
"But if our offers are rejected it means we will enter another stage. This is not our choice. We do not want it."
Russia and Ukraine have been locked for months in a dispute over the price of Russian gas supplies and Ukraine's debt for previous deliveries.
Moscow has threatened to turn off the tap if Ukraine fails to settle the multibillion dollar debt, but repeatedly pushed back the deadline after Ukraine paid off part of the debt.
European Union-brokered talks between the two countries in Brussels on Wednesday failed to reach a compromise over price.
The bruising gas dispute comes amid continuing fighting in eastern Ukraine, where government forces have battled pro-Russian rebels for two months.
The insurgents have pushed for joining Russia following Moscow's annexation of Ukraine's Crimean peninsula in March, but Putin has ignored their appeal in an apparent bid to avoid another round of crippling Western sanctions.
Putin also seemed eager to avoid cutting off gas to Ukraine, a move that would likely disrupt shipments to European customers via pipelines crossing the Ukrainian territory.
He emphasized Wednesday that the latest offer would restore the price Ukraine had under pro-Russia President Viktor Yanukovych.
In December, Russia offered Ukraine an even lower price of $268 as it sought to give a financial lifeline to Yanukovych, who was facing massive protests triggered by his decision to ditch a pact with the European Union and opt for closer ties with Moscow.
After Yanukovych was chased from power in February, Russia denounced his ouster as a "coup" and annulled all gas discounts, bringing the price back to $485 per 1,000 cubic meters in line with a 2009 contract.
Ukraine has refused to pay for Russian gas, demanding that Moscow lowers the price.
Ukraine's Energy Minister Prodan told reporters after the talks in Brussels that the price discount offered by Russia isn't enough and demanded an even lower price.
He said the Ukrainian government now believes that arbitration is the best option to solve the dispute.
Prodan, however, added that Ukraine is open to talks to hammer out a temporary price while arbitration is proceeding. EU Energy Commissioner Guenther Oettinger, who is involved in the talks, said he hopes the parties will make progress in the next 48 hours.
"I can see movement on both sides, and both sides will need to continue to move," he told reporters.
"There are differences of opinion ... and we're talking about billions."
Oettinger said that Putin and Ukrainian President Petro Poroshenko are also discussing the issue.
On the EU's behalf, he has drawn up a draft agreement that he hopes both Russia and Ukraine can ultimately agree to, including a temporary "$385 minus" price tag.
He said the final price will depend on two factors: the volume of Russian gas purchased by Ukraine, and the length of the agreement, which he has suggested should be 15 months.
That would be enough for the Ukraine to see through the winter of 2014-15 and allow it to build up its reserves for another winter.
Ukrainian Prime Minister Arseniy Yatsenyuk earlier Wednesday said that Kiev initially rejected the Russian offer because there was no guarantee that it would last.
Putin and Novak responded by saying that Russia was ready to guarantee the discounts would remain in place for one year.
Gazprom, Russia's gas giant, earlier on Wednesday gave Ukraine another week before it would start demanding prepayment for gas, without which it has threatened to cut off supplies.
Gazprom CEO Alexei Miller told Russian news agencies after Brussels-brokered talks with Ukraine in the early hours on Wednesday that the deadline would be pushed forward to next Monday.