The WerteUnion, a nationwide federation of Conservatives blasted the German leader for disregarding the will of the people and pressing ahead with her own agenda.
In a strongly worded statement it accused Mrs Merkel of trying to change the Christian country’s roots and urged her to resign.
It also blasted her for allowing open immigration and causing widespread electoral losses in the Lower Saxony region.
Alexander Mitsch, the Chairman of the WerteUnion told Tichys Einblick magazine: “As a consequence of the renewed defeat we demand not only the resignation of Angela Merkel as a party chairman, but also a clear roadmap for handing over to a new chancellor candidate of the Union.
“A new chancellor or a new chancellor needs a reasonable period of about two years to set his own accents and to prepare a chancellor’s bonus.
We reject a new candidacy of Angela Merkel in the most decisive way.”
WerteUnion made its comments after the Minister of the Interior Thomas de Maiziere announced the Government was considering a Muslim public holiday in the country.
The Conservative group said that the decision must have been made in coordination with Mrs Merkel in advance, despite a large swathe of the German public being opposed to it.
Germany is home to around 4.5 million Muslims, many of whom have a Turkish background.
At least a million migrants who have arrived in the country from the Middle East and elsewhere over the last two years are also Muslims.
Mr Mitcsch added: “For the forthcoming coalition negotiations, we demand a “red line” in the form of a restrictive immigration policy under the motto “limit and control immigration”.
“In particular, the immigration system, which has been going on for decades, has to be stopped in the social system and a “minuscountry” has to be pursued.
Mrs Merkel is still attempting to form a coalition following the Bundestag elections in September.
Talks on a potential partnership between Mrs Merkel’s conservatives, the pro-business Free Democrats and traditionally left-leaning Greens will start on Wednesday.
However the proposal for a Muslim public holiday caused a widespread backlash from fellow conservatives involved in the coalition talks.
Alexander Dobrindt, a senior figure in the Christian Social Union (CSU) said that Germany’s Christian heritage was non-negotiable.
He said: “We won’t consider introducing Muslim public holidays in Germany.”
The German constitution states that Germany’s individual states decide on religious public holidays.
But Hamburg and Bremen in the north have signed agreements with some Muslim organisations so that Muslim pupils can have time off school and workers could take holidays for festivals important to Islam.