"I call on the kidnappers to immediately release the three Germans," she said in Sunday's edition of Bild newspaper, adding that Berlin would not allow itself to be blackmailed.
The German government "will do everything to secure their release and is working directly with the Turkish authorities" on the case, Merkel said.
She said she would discuss the issue when she meets Turkish Prime Minister Recep Tayyip Erdogan at a Mediterranean summit in Paris on Sunday.
On Friday, a spokesman for the German foreign ministry called for the "immediate and unconditional release" of the three Germans, who the Kurdish Workers Party (PKK) seized from Mount Ararat in Turkey late on Tuesday.
The group said in a statement on Thursday that the tourists would not be released "unless the German state announces that it has given up its hostile policies against the Kurdish people and the PKK."
German Foreign Minister Frank-Walter Steinmeier at the time rejected demands for a change of policy towards the PKK in exchange for their freedom.
The PKK, considered a terrorist organization by Turkey, the European Union and the United States, has been banned in Germany since 1993, and German authorities have taken legal action against several of the group's leaders.
According to a report in Monday's edition of Der Spiegel weekly, the Kurdish rebels warned Germany about the "negative consequences" of its policy towards Kurds at the end of June in a message sent via its embassy in Turkey.
The PKK's executive council called on the government to give up "its hostile policy towards the Kurdish people and its liberation movement" or take responsibility for "the negative consequences", the magazine said, without naming its sources.
Shortly afterwards, Turkish police informed their German colleagues of heightened activity within Kurdish circles in Turkey and warned of the likely risk of kidnappings or attacks.
German police passed on the information to the interior ministries of several countries, according to Der Spiegel.
Secretary of state for the interior August Hanning acknowledged to the magazine: "We will probably also have to prepare ourselves for new dangers on German soil."
The PKK has waged a bloody struggle for self-rule in Turkey's Kurdish-populated southeast since 1984. While it has kidnapped people in the past, among them soldiers, police and tourists, it is not a regular occurrence.