Medvedev, speaking to reporters on a visit to Spain on Tuesday, also insisted that the two issues were separate.
"If we are talking about any "swap" [Iran for missile defence], this is not how the question is being put. This would not be productive," he said.
A spokeswoman for the Russian president said that Obama's correspondence was a response to an earlier Russian letter.
Medvedev said he had talked with Obama on the phone and had exchanged letters with him, but that there had not been talk of "some kind of trade-off, or quid pro-quo".
"No one is linking these issues to some kind of trade-offs, particularly on the Iranian issue," Medvedev said.
"We are already working in close contact with our US counterparts on
the Iranian nuclear issue."
But he added: "If the new administration shows common sense and offers a new [missile defence] structure which would satisfy European [needs]... and would be acceptable for us, we are ready to discuss it."
"I count on positive signals we are now receiving from Washington translating into agreements," he said.
White House officials earlier told the AFP news agency that Obama had "sent a letter to Medvedev covering a broad range of topics, including missile defence and how it relates to the Iranian threat".
'No concrete proposals'
Natalya Timakova, Medvedev's spokeswoman, said: "We have received this letter. It was, in fact, a reply to a letter from Medvedev sent to Obama after his appointment.
"The letter contained an assessment of the situation, but there were no concrete proposals about any mutually binding decisions."
Russia has opposed the deployment of a US missile defence system in Poland and the Czech Republic, which was proposed by the administration of George Bush, the former US president.
Hillary Clinton, the US secretary of state, said the defence system "has always been intended to deter any missile that might come from Iran".
She said the issue would be discussed when she meets Sergei Lavrov, the Russian foreign minister, this week.
Obama and Medvedev are expected to meet at the G20 economic summit in London next month.