Speaking to reporters as he greeted Merkel at his palm-lined residence on the Black Sea, Medvedev congratulated Merkel on news that Germany had emerged from recession and said Russia was working hard to do the same.
"We should think how, by strengthening our bilateral economic strategic ties, we could help our economies and people overcome consequences of this difficult global crisis and emerge stronger," Medvedev said.
Merkel replied that she had been "very happy" at Thursday's German economic news and confirmed that her meeting with Medvedev - their second in just a month, and third this year - would centre on economic issues.
"I believe that we need to use every chance that the global financial crisis offers to develop the Russian-German economic relations," the German chancellor said.
The two leaders were expected to hold a news conference at 4:00pm (1200 GMT).
Merkel is widely expected to remain at the helm of Europe's most powerful economy following elections on September 27 and Medvedev said he and the German leader would also discuss international issues.
Speaking on German radio on the eve of her trip to Russia, Merkel delivered some criticism for Medvedev, albeit very gentle, on the latest murders of human rights activists in Chechnya.
"I want to believe that the subject is close to his heart," she told the Deutschlandradio Kultur station. "But he has to act."
But while Merkel aides said she may raise rights issues with Medvedev, both sides made clear Friday's meeting was about business, including deals on carmaker Opel and plans for Russian investment in struggling German firms.
Russia's priority at the talks will be to cement a deal in which its largest lender, state bank Sberbank, in a consortium with Canadian automaker Magna would buy a stake in Opel, the struggling European unit of General Motors.
The two will also discuss Russian investment in ailing German firms like Wadan dockyards and insolvent Dresden-based Qimonda chipmaker, part of Infineon electronics company, the Kremlin said in a statement ahead of the visit.
Both Qimonda chipmaker and Wadan dockyards are located in eastern Germany - Merkel's constituency - and are struggling with the prospect of mass layoffs.
"The projects in question can become a starting point for strategic alliances between Russian and German high-tech companies in the auto industry, shipbuilding and electronics," the Kremlin said.
A report Friday in the Russian business daily Kommersant said that Russian conglomerate Sistema could buy a stake in Infineon.
The report did not say how much Sistema was prepared to spend, but said the topic would be discussed by Merkel and Medvedev.
In a note to clients, Russian investment bank Renaissance Capital said a deal for a Russian firm to buy a stake in Infineon "would be political" and "would not be the best use of liquidity in the current environment."
A Sistema representative, speaking to AFP on condition he not be named, said the company was not involved in discussions on the plan.
"We are aware that such an idea exists," the representative said. "The idea comes from the two leaders."
Kommersant and another business daily, Vedomosti, said the deals under discussion would not make much economic sense for Russia but could help Merkel ease social tension stemming from the prospect of mass layoffs in Germany.
"Moscow is trying to help Angela Merkel and one of the reasons is because her position is extremely important for the fate of Gazprom's Nord Stream project," Kommersant said.