Medvedev said: "In light of the growing negative trends in international affairs, frank dialogue between Russia and Germany is very useful and will continue on a wide spectrum of subjects.
"The two countries' common interests are much greater than their differences. The unique nature of the Russian-German relationship has the capacity to find a compromise and surmount the problems that arise."
There has been friction in the past between Merkel, a fluent Russian speaker who grew up in communist east Germany, and Medvedev's predecessor Vladimir Putin, a former KGB agent in Dresden.
Merkel has been outspoken in her criticism of alleged human rights violations in Russia and what she says is growing authoritarianism there.
Ulrich Wilhelm, a German government spokesman, said Merkel would be no less direct with the new president but had been encouraged by a few initial statements by Medvedev, such as his plans for judicial reforms.
Wilhelm said: "We will debate intensively, as we did with his predecessor President Putin, which further possibilities we both see for moving these international problems toward a resolution.
"Moreover we have very intensive and steadily growing economic cooperation, not only in the area of energy but also in a range of other sectors, that we want to develop further."
Germany is anxious to see whether Medvedev will chart a more moderate course and wants to expand trade with the oil- and gas-rich nation while ensuring energy supplies, which make up 70 per cent of German imports from Russia.
In 2007, Russian oil and gas imports cost Germany around $31bn, making up the vast majority of its total imports which came to $44bn.
Exports to Russia grew by 20 per cent last year compared with the figure for 2006, and trade between the two countries has continued to expand this year.
The German media has said Berlin should at first give Medvedev the benefit of the doubt.
"Germany should do everything it can to get further positive signals from Moscow," Der Tagesspiegel, a centre-left newspaper said in an editorial.
"It is high time the bilateral relationship was redefined, to focus on what the two countries want to achieve together in future. Let's take Medvedev at his word."
A week after his inauguration on May 7, Medvedev underlined the importance of a strategic partnership between Russia and Germany, Europe's biggest economy, when he announced the trip to Berlin.
Merkel visited Medvedev in Moscow after his victory in presidential elections in March and Frank-Walter Steinmeier, the German foreign minister, was the first foreign dignitary received by the new president after he took office.