Russian President Vladimir Putin met the leaders of both countries during a trip to China last week and Miller was among the business chiefs who accompanied him on the trip.
Gazprom is looking to compensate for the loss of most of its markets in Europe since the start of Russia's war in Ukraine, largely due to explosions that severely damaged its Nord Stream pipelines under the Baltic Sea last year. Investigations have yet to establish who was responsible.
Hungary is the only member of the European Union whose leader, Prime Minister Viktor Orban, has maintained friendly ties to Putin since the invasion of Ukraine in February 2022. It is also a member of NATO.
Orban told Putin when they met in Beijing on Tuesday that Hungary never wanted to oppose Russia and was trying to salvage bilateral contacts. The U.S. ambassador to Hungary said Orban's decision to go ahead with the meeting was "troubling". Estonia's prime minister said images of them shaking hands were "very, very unpleasant".
Hungary is seen as the key potential opponent to a decision due in December on whether to open EU accession talks with Ukraine, which would require the unanimous backing of the bloc's 27 members.
The EU as a whole has sharply reduced its dependence on Russian energy in response to the Ukraine war but TASS quoted Gazprom's Miller as saying in a TV interview that additional gas supplies to Hungary this year amounted to 1.3 billion cubic meters.
"And we have an agreement that we will supply additional volumes on an ongoing basis in the coming winter", he said.
Miller said daily demand from China was also above contracted levels.
"We regularly supply additional volumes to the Chinese market. Moreover, we have been doing this for several years now. This year, I think (the extra amount) will be 600 million cubic meters of gas," he was quoted as saying.
