"I do not think that with him the partnership will be more simple," Putin said after talks with Merkel just outside Moscow.
Merkel was due later to become the first Western leader to meet with Medvedev since his controversial landslide election win on March 2 to replace Putin, who is expected to stay on as prime minister.
The German leader said there was no alternative to cooperation between Moscow and EU powers, which have frequently clashed over democracy in Russia and security concerns during Putin's tenure.
"Germany and Russia, Europe and Russia, are interdependent. We must find a way to go forward together. There are many things to do," Merkel said at Putin's residence.
Merkel, who was expected to discuss tensions over Kosovo, Iran's nuclear programme, and Russian energy exports to Europe, also alluded to East-West strains.
"Since I've been in power we've found a way to discuss together and to raise critical issues in an open and sincere way," she said. "It's always a joy and sometimes a challenge."
Putin described Germany as "the most important partner for us in Europe and in the world."
Earlier this week Merkel congratulated Medvedev on his landslide victory, while expressing concern about alleged election irregularities. "The chancellor would like to form an impression of what the Russian political landscape will look like in future," German government spokesman Ulrich Wilhelm said.
Tensions between Moscow and the West have risen sharply in the last year amid disagreements over human rights in Russia and Moscow's angry opposition to a US plan for a missile defence system in central Europe.
“The chancellor would like to form an impression of what the Russian political landscape will look like in future,” German government spokesman Ulrich Wilhelm said ahead of Merkel's one-day visit to Russia.
“She is looking forward to learning more about Dmitry Medvedev's stated plans to entrench the rule of law and to modernize the Russian state and economy,” he said.
On a lighter note, Putin joked with Merkel that he had given presents to his wife for International Women's Day, which was celebrated widely in Russia on Saturday, and would breakfast with her.
"Have you prepared breakfast for your wife this morning?" Merkel asked with a smile.
"I gave her presents, but we will have breakfast together," Putin responded, despite the fact that their meeting started at around lunchtime.