"Issuing permission for a prosecution to go ahead... does not mean pre-judging the defendant nor a premature decision about the boundaries of freedom of art, the press, or opinion," Merkel said.
She added that the government planned to abolish paragraph 103 of the criminal code, the law against insulting foreign heads of state, with effect from 2018, saying that it was "disposable for the future".
The law is a hangover from German legal codes dating back to the 19th Century that have never been repealed.
It is commonly known in Germany as the Shah Paragraph, after the Iranian Shah Mohammed Reza Pahlavi used it to try and suppress criticism from the within the Bundesrepublik (Federal Republic of Germany).
Erdogan called on the German government to invoke the law after Böhmermann read out a 'slanderous poem' on his weekly satire show Neo Magazin Royale, broadcast by public television channel ZDF.
Böhmermann's poem accused Erdogan, among other things, of having sex with goats and watching child pornography.
He declared that the poem was deliberately insulting in a bid to show Erdogan the limits of free speech, after the Turkish leader complained of a comparatively mild satirical song shown by rival satire show Extra 3.
'Courts should decide'
"The situation of the media in Turkey and the fate of individual journalists fill us with great concern, as do limitations on the right to demonstrate," Merkel acknowledged in a nod to Turkish President Recep Tayyip Erdogan's widely criticized moves to consolidate his power at home.
"Towards other states, we act to protect basic rights like freedom of opinion, freedom of art, and freedom of the press. We demand their respect and protection from Turkey as well. We demand that because we are convinced of the strength of the rule of law," she went on.
But the Chancellor said that in Germany, "prosecutors and courts, not the government, should have the last word" on whether someone had broken the law.
Merkel also made clear that there had been a significant battle of opinion within Germany's ruling coalition.
Voices from the Chancellery, the Interior Ministry, the Justice Ministry, and both Merkel's Christian Democratic Union (CDU) and the Social Democratic Party (SPD) had weighed in.
The government's decision to allow for a prosecution, which is a prerequisite of paragraph 103, was met with an immediate avalanche of criticism on social media.
The head of the opposition in the German parliament, Sahra Wagenknecht of the Left Party, described it as "an unbearable kowtow. Merkel is knuckling under to Turkish despot Erdogan and sacrificing press freedom in Germany".
Elke Grohs, head of the influential private broadcaster n-tv, described it as an "act of submission to Erdogan".
"I think this is a wrong decision by the Chancellor," SPD national board member and Hamburg-based MP Niels Annen wrote.
Ich halte das für eine falsche Entscheidung der Kanzlerin.— Niels Annen (@NielsAnnen) 15. April 2016
"I think this decision is wrong. Prosecuting satire because of lèse-majesté does not belong in a modern democracy," SPD leader in the Bundestag (German parliament) Thomas Oppermann agreed.
Ich halte die Entscheidung für falsch. Strafverfolgung von Satire wg "Majestätsbeleidigung" passt nicht in moderne Demokratie.@janboehm— Thomas Oppermann (@ThomasOppermann) 15. April 2016
Tobias Huch, a politician with the Free Democrats, went as far as to call for Merkel to leave her job, writing “Angela Merkel is no longer bearable as Chancellor”.
But others backed Merkel's arguments.
"The Böhmermann case is now where it belongs: with the justice system. And politics is out. That's how a state with the rule of law works," wrote journalist Udo Stiehl.
Der Fall #Boehmermann ist jetzt da, wo er hingehört: Bei der Justiz. Und die Politik ist raus. So funktioniert ein Rechtsstaat.— Udo Stiehl (@udostiehl) 15. April 2016
"I would rather have freedom of satire confirmed by the courts than confirmed by the mercy of the government," author Philip Meinhold agreed.