The exchange between the US and Russian presidents was picked up by microphone without either leader apparently knowing.
Mr Medvedev, who steps down in May, said he would pass on Mr Obama's message to his successor Vladimir Putin, according to an audio recording of comments the two leaders made during a meeting in Seoul, South Korea.
Mr Obama says: "On all these issues, but particularly missile defence, this, this can be solved but it's important for him to give me space."
Mr Medvedev replies: "Yeah, I understand. I understand your message about space. Space for you …"
Mr Obama retorts: "This is my last election. After my election I have more flexibility."
And Mr Medvedev finishes: "I understand. I will transmit this information to Vladimir [Putin]."
Once they were made public, the White House said Mr Obama's words reflected the reality that domestic political concerns in the both the US and Russia this year would make it difficult to fully address their long-standing differences over the contentious issue of missile defence.
Mr Obama, should he win re-election, would not have to face voters again.
"Since 2012 is an election year in both countries, with an election and leadership transition in Russia and an election in the United States, it is clearly not a year in which we are going to achieve a breakthrough," White House deputy national security adviser Ben Rhodes said.
Tensions over missile defence have threatened to upend the overall thawing of relations between the U.S. and Russia in recent years.
Both leaders acknowledged as much in their public statements following their meeting. Obama said there was "more work to do" to bridge their differences; Mr Medvedev said each country had their own positions on missile defence, but there was still time to find a solution.
Russia has been strongly critical of plans for US-led Nato missile defence in Europe. Russian officials believe the planned missile shield would target Russia's nuclear deterrent and undermine global stability, while the US insists the planned missile shield is intended to counter threats from Iran.
Mr Putin said earlier this month that Washington's refusal to offer Moscow written guarantees that its missile defence system would not be aimed against Russia deepened its concerns.
Putin won elections held earlier this year and will return to the presidency later this spring. He is expected to name Medvedev prime minister.
The US and Russia have also clashed recently over their approach to dealing with violence in Syria. The U.S. has sharply criticised Russia for opposing UN Security Council action calling on Syria's president to leave power.
Mr Obama said Monday that despite past differences on Syria, he and Medvedev agreed they both support UN envoy Kofi Annan's efforts to end the violence in Syria and move the country towards a "legitimate" government.
The apparent gaffe is the second such incident in less than six months that Mr Obama has been involved in.
In November, Mr Obama and Nicolas Sarkozy of France inadvertently broadcast a private exchange, during which the French president said he could not "bear" Benjamin Netanyahu, the Israeli prime minister.
Mr Obama in return said: "You may be sick of him, but me, I have to deal with him every day."