Speaking to the German Council of Foreign Relations in Berlin the same day, the Kremlin leader also called for a sweeping new European security pact to replace Cold War-era bodies.
In content, both statements were in fully keeping with the assertive policy Moscow has adopted in dealing with the West in recent years.
What was different was the tone. Rather than employing the bellicose rhetoric that was the trademark of his predecessor, Vladimir Putin, Medvedev instead struck a conciliatory note.
"The end of the Cold War provided conditions for building truly equal cooperation among Russia, the European Union, and North America as three branches of European civilization," Medvedev said. "I'm confident that Atlanticism as the only principle has become obsolete historically. Now, we should talk about the unity of the entire Euro-Atlantic region from Vancouver to Vladivostok."
Few expect the idea of replacing NATO with a new security alliance to gain any traction, but the mood music was noteworthy.
Medvedev's language, reminiscent of Soviet leader Mikhail Gorbachev's perestroika-era musings about a "common European home," contrasts sharply with the Cold War bombast often used by ex-President and current Prime Minister Putin.
The new Kremlin head will have ample opportunity to polish his performance in the days ahead. Upon returning home from Germany, Medvedev is due to huddle with a potential adversary, Georgian President Mikheil Saakashvili, in an attempt to defuse escalating tensions between Moscow and Tbilisi over the breakaway region of Abkhazia.
Those discussions take place on the sidelines of the June 6-7 St. Petersburg summit of leaders from the Commonwealth of Independent States (CIS), where Medvedev will hold a long list of bilateral talks. He will also preside over the city's 12th annual International Economic Forum, the country's premier business event, where he will try to woo foreign investors.
But even as the new Kremlin leader embarks on his frantic wave of fence-mending diplomacy, his onetime patron and now nominal subordinate, Putin, is doing little to tone down his anti-Western rhetoric criticizing the West over Kosovo, Iran, and NATO expansion. During a recent visit to France, for example, Putin accused the United States of behaving like "a frightening monster" abroad.
As a result, Moscow is rife with questions about just who -- Medvedev or Putin -- is really in charge of Russian foreign policy.
Much of the speculation is fueled by reports that veteran diplomat Yury Ushakov, currently Russia's ambassador to the United States, has been recalled to Moscow to serve as Putin's deputy chief of staff in charge of foreign affairs.
Some observers suggested the move might drain power from Sergei Lavrov, who has served as foreign minister since he was appointed by then-President Putin in 2004, and remains in the post under Medvedev.
Analysts call the move a clear signal that Putin has no plans to give up the reins in foreign affairs.
"It is clear that the management of Russian foreign policy is undergoing a restructuring," Nikolai Zlobin, the director of the Russia and Eurasia Project at the Washington-based World Security Institute, tells RFE/RL's Russian Service. "And Ushakov's appearance in Moscow is an important factor in that process. I think the idea of such a person joining the government secretariat is witness to the fact that definite foreign-policy functions are being moved there."
'Good Cop, Bad Cop'
Nevertheless, Medvedev remains the main player in Russian foreign policy -- at least on paper.
And with the emerging diarchy, many Russia-watchers are unsure what they are witnessing -- a competition, or an elaborate partnership, with Putin playing the tough guy to Medvedev's soothing conciliator. Nikolas Gvosdev, a Russia expert at the Nixon Center in Washington, says it appears to him that Putin and Medvedev are coordinating their foreign-policy moves.
"I think it leans to 'good cop, bad cop.' But I also think they're attempting to divide -- and it may not work -- different aspects of foreign policy," Gvosdev says. "That is, Medvedev is your go-to business guy, who will sign contracts, and talk up the positives of cooperation and how we can all make money. And Putin is the heavy who comes in and says let's talk nuclear security."
In Berlin, Medvedev certainly acted like a "go-to business guy" -- talking up trade and economic ties in a joint press conference with German Chancellor Angela Merkel.
"The key subjects of our discussion were trade, economy, and bilateral business cooperation. Trade has increased significantly in recent years," Medvedev told reporters. "It has exceeded the threshold of $50 billion and, of course, we don't want to stop there. I'm sure there is every opportunity to expand our trade and economic cooperation."
While Medvedev said he was "concerned about the current trend of narrowing mutual understanding in Euro-Atlantic policies," he also went out of his way to praise his hosts for taking a "constructive position" in helping push forward a stalled partnership agreement between Russia and the European Union.
Despite Medvedev's high profile in recent days, analysts agree that, at least for now, Putin remains in charge -- a fact that was driven home by Ushakov's appointment.
Ushakov, who was a candidate for foreign minister back in 2004, is widely viewed as a heavyweight in the Russian foreign-policy community. His appointment to Putin's team was bound to raise eyebrows.
Moreover, the move comes on the heels of a high-profile visit by Putin to France last month, in which he had dinner with President Nicolas Sarkozy in the Elysee Palace.
Analysts say Putin's Paris trip was a sign that the West still views Putin as top dog in foreign policy.
"The example of the visit to France shows that the West hasn't changed anything and accepts the status quo. France received Putin as a head of state, not the head of government -- and nobody hid this," Fyodor Lukyanov, editor of the Moscow-based journal "Russia In Global Affairs," tells RFE/RL's Russian Service.
Such sentiments are not confined to the French. Gvosdev notes that the U.S. foreign-policy community still sees Putin as Russia's dominant policymaker.
"Here in Washington, the default assumption among most people is that people should continue to do business with Putin, which I find interesting," Gvosdev says. "He is the go-to guy, he is the one that the U.S. should sort of stay in touch with."
During his Paris trip, Putin played the part. He was his old combative and confident self in an interview with the daily "Le Monde," in which he harshly denounced NATO expansion and criticized the West's policy toward Iran.
At a press conference with French Prime Minister Francois Fillon, he took a swipe at what he described as France's human rights problem -- criticizing conditions in France's prisons and asking: "Is everything all right there? Let's dig into that -- I am sure there are many problems."
Gvosdev says there are "some elements of competition" in the Putin-Medvedev relationship, but that for now, such elements are "muted."
Since taking office as prime minister in early May, Putin has made moves that are widely seen as bolstering the government's authority. He has established a new executive body, the presidium, comprised of seven deputy prime ministers and seven other ministers, which will meet once a month to coordinate policy. Three of the members of the presidium -- Foreign Minister Lavrov, Defense Minister Anatoly Serdyukov, and Interior Minister Rashid Nurgaliyev -- also report directly to Medvedev.
In the short term, Gvosdev says the tango between Putin and Medvedev is working because they are largely in agreement on most matters of policy, despite the president's more conciliatory tone.
"What they have created with this new super cabinet is a sort of dual-key system where on most matters of policy the two of them and their people have to sign off," Gvosdev says. "That arrangement only works if they are all on the same page. We may see greater competition in the future. I think that right now it's not there yet."
RFE/RL's Russian Service contributed to this report