Merkel was speaking after Monday's abduction and murder of the head of Let's Save the Generation, Zarema Sadulayeva, and her husband, which she called "absolutely unacceptable".
On Friday, she will hold talks with Medvedev at his summer residence at the Black Sea resort of Sochi.
At their last meeting on July 16 in Munich, eastern Germany, Merkel called on him to launch an investigation into the murder of Natalya Estemirova, one of the best known rights activists in Chechnya, who had been killed that month.
"I think that everything must be done on the Russian side to arrest the murderers... of a courageous woman," Merkel said at the time.
Medvedev himself vowed at the time that the crime would not go unpunished.
Unidentified armed and masked men, two in civilian dress and three wearing military fatigues, abducted Sadulayeva and her husband Alik Djibralov after storming the offices of her young people's NGO in Grozny.
Their bullet-riddled bodies were found in the trunk of their car Tuesday.
Russian prosecutors have opened an investigation into the killings.
The EU presidency on Wednesday condemned the murders, calling for an investigation and urging Moscow to ensure the safety of such activists.
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