He emerged from hosting an international summit on the gas crisis encouraged by comments from the Ukrainian side, noting that Kiev had offered to make advance payments for Russian gas supplies.
"I am sure that in the near future we will solve the transit problem," Medvedev said at a news conference after the meeting.
"But, certainly, we need to solve the question of the price of gas for Ukraine, and for this we need to sit down at the negotiating table," he said. "Our Ukrainian partners expressed their intention to make advanced payments on a number of issues. It is very good and we welcome this."
The Russian president also said that Ukraine was capable of paying European prices for Russian natural gas supplies.
"Ukraine must pay European prices for gas. It is absolutely normal and this is our position," Medvedev said. "Our other partners pay this money and Ukraine is able to pay it."
After the summit, the Russian and Ukrainian prime ministers continued discussions on resolving the dispute. Vladimir Putin and Yulia Tymoshenko had briefly met one-on-one before attending the international gathering at the Kremlin.
Medvedev said he believed Tymoshenko had the mandate required to agree the terms for a deal between the two countries.
The Russian president said his Ukrainian counterpart, Viktor Yushchenko, had told him that "the positions of the president and prime minister of Ukraine were absolutely identical."
"We shall see," Medvedev said.
Spokesmen for both Gazprom and the Ukrainian Embassy in Moscow told journalists that a transit gas deal could be agreed on Saturday.
"We are hopeful. The main thing is to ensure the transit of gas," said Sergei Kupriyanov, the Russian energy giant's official spokesman.
Also speaking to journalists on the sidelines of the summit, Ukrainian Embassy official Oleh Voloshin said the gas transit issue "could literally be solved today."
He warned, however, that the fate of relations between Russia and Ukraine hinged on an agreement for supplies of Russian gas to Ukrainian consumers.
"Stable cooperation between Russia and Ukraine in the gas sphere is impossible without a decision on the question of gas deliveries to Ukraine," he said, adding that this did not mean that if Ukraine "did not receive gas from Russia it would block gas transit."
Medvedev said Russia was willing to help Ukraine arrange a $1 billion credit from a European bank to get supplies flowing again.
He also stressed that Russia was not concerned over the volumes of technical gas Ukraine said it needed to restart transit operations, it just wanted to be "sure that the gas going into a pipeline will reach European consumers, instead of being used for internal needs."
Russia suspended supplies to Ukraine on January 1 after the former Soviet neighbors failed to agree on debt and prices for 2009. The halt in shipments to the EU came a week later, and an EU-brokered deal signed on Monday was not enough to resume deliveries, even though international monitors were deployed to ensure gas would not be siphoned off.
