The remarks were published by RIA news agency the morning after Washington handed over written responses to a set of security demands that Moscow made last year as it built up troops near Ukraine, fuelling fears of a looming invasion.
Russia, which denies planning an attack, has not yet commented publicly on the content of the U.S. written responses.
"It's obvious here that the most important and single route is actually to come to agreement on security guarantees, (through) political-diplomatic means, negotiations, the use of the principle of the indivisibility of security..." Medvedev was quoted as saying.
He said the idea of a conflict between Russia and Washington over Ukraine would be a "catastrophic scenario" and voiced alarm that "hot heads" in the United States and NATO were even imagining such a scenario. "I'm counting on that never happening," he said.
His comments fit into a pattern of softer, more defensive rhetoric out of Moscow after weeks of hawkish remarks by senior officials during the crisis.
"It's another matter that there are plenty of people who are making money from this, speculating on it. Some people are doing it out of ignorance, others because they are pursuing a specific political line," he said.
Medvedev, a close ally of Russia's paramount leader Vladimir Putin and who served as president from 2008-2012, pointed to an elderly U.S. senator who he said had publicly entertained the possibility of a limited Russian-U.S. nuclear confrontation. He did not name the senator.
Medvedev is deputy chairman of Russia's Security Council.
(Reporting by Maxim Rodionov; writing by Tom Balmforth; Editing by Toby Chopra)
