The German Chancellor, now in her third term, had been urged to step down from her role in the CDU amid plunging approval ratings.
The 64-year-old engaged her critics yesterday after saying she would run for re-election at the party congress in December.
Alexander Mitsch, a senior figure on the CDU’s conservative wing, said Mrs Merkel should quit for the sake of the party and country.
He said: “It would be better in the interest of the CDU and Germany if it paves the way for the much-needed renewal of personnel.
“Mrs Merkel should draw the consequences of the mistakes made by her, especially in the asylum policy, and the resulting poor poll numbers.
“This would be an opportunity to re-integrate the party’s conservative and pro-business wing.”
But Ralph Brinkhaus, the head of the CDU and Christian Social Union (CSU) in the German parliament, threw his weight behind Mrs Merkel.
He said: “I assume that she will compete, and I would endorse that, because a head of government also needs the backing of the party.”
Mr Brinkhaus replaced Volker Kauder, a long-standing ally of Angela Merkel, in the post earlier this week after a party vote.
The shock poll dealt a further blow to the Chancellor’s waning authority, as she struggles to unite Germany’s coalition.
Social Democratic politician Thomas Oppermann said the move was an “uprising against Merkel”.
Alexander Graf Lambsdorff, from Germany’s Free Democratic Party, said it was “the beginning of the end of the grand coalition”.
Daniel Guenther, the premier of northern state Schleswig Holstein, added: “The vote shows a desire for renewal.
“There was clearly a certain discontent over national politics.”
And a CDU adviser said: “Kauder was the first domino to fall, but there might well be more. This could be just the start.
“I can imagine the entire senior party leadership coming under pressure to resign, and that includes Merkel.”