But the topic of human rights also figured highly in their conversations after the killing of Natalya Estemirova, from Russian rights group Memorial, found murdered on Wednesday after being abducted in Chechnya.
Merkel greeted the Russian president with full military honours at a picturesque castle in the southern city of Munich for full governmental consultations between key ministers of both governments.
The two leaders held private talks for over an hour before being joined by top officials including the ministers for the interior, education, environment and economy, Berlin said.
The get-together encompassed foreign policy questions such as Iran and North Korea, but the main business of the day was the two countries' substantial and growing ecomomic ties.
Germany is widely considered Russia's closest ally in western Europe and is its biggest trade partner, and the two countries inked a raft of economic partnership deals in Munich.
Almost 40 percent of German gas imports come from Russia, some 4,600 German firms have subsidiaries in Russia and every fourth machine imported by Russia has a "Made in Germany" label. But after a string of disruptions in gas supplies because of disputes between Russia and transit country Ukraine, Merkel was also expected to press Medvedev on energy security.
"Russia and Germany understand each other here, both want to reinforce Ukraine as a reliable transit country for gas deliveries to Europe," Timofei Bordachev, director of the Centre for Comprehensive European and International Studies in Moscow, told AFP.
Another pressing economic issue that featured was the possible takeover of troubled German carmaker Opel by Russian-backed Canadian auto parts maker Magna International.
Berlin agreed in late May to support a bid for a majority stake in Opel by Magna, which has teamed up with state-owned Russian bank Sberbank and Russia's second-largest auto maker GAZ.
However, Opel's parent company General Motors has also received interest from Brussels-based investment group RHJ International and from China's Beijing Automotive Industry Company (BAIC), throwing the deal into some doubt.
Prikhodko said Medvedev would push the deal in Munich. "We'll speak out in support (of the deal) and we'll call on (Germany) to support it too... It's a useful deal," he said.
On the killing of Estemirova, Merkel said that it had "played a role" in her talks with the Russian president, who she said had assured her that "everything would be done to clear everything up."
Estemirova was the latest in a string of campaigners to be killed in Russia, with the 2006 murder of investigative journalist Anna Politkovskaya the most notable, and Western governments were quick to express their outrage.
For Germany, Foreign Minister Frank-Walter Steinmeier said late Wednesday he was "disturbed" by the murder, adding that he condemned "in the strongest possible terms" what he termed a "cowardly act."