Mrs Merkel said on Saturday that the conservatives must end their in-fighting to reverse slides in the polls before two regional elections this month.
The CDU and their Bavarian Christian Social Union (CSU) sister party have struggled to maintain a united front on immigration policy and the fate of the scandal-hit domestic intelligence agency.
Polls indicate the CSU will lose its absolute majority in the Bavarian parliament in an election in the southern state on October 14 expected to bleed support to the ecologist Greens and the far-right Alternative for Germany (AfD) party.
Support for Mrs Merkel is also projected to fall, to around 29 percent, in an election in the state of Hesse two weeks later.
Mrs Merkel said in a speech: “I know that through our dispute we have contributed to making the polls look as they do.
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“Voters don’t appreciate it if we argue and they don’t even understand what we’re arguing about.”
Mrs Merkel’s authority has been waning since an inconclusive election in September last year that produced the worst result for her conservatives since 1949.
Her first attempt to form a government with the Greens and Free Democrats (FDP) was unsuccessful, forcing her to turn to the centre-left SPD to secure a fourth term.
She has since faced calls from her own party to name a successor.
The CDU/CSU youth wing on Saturday demanded a constitutional amendment to limit the number of terms that a chancellor can serve to three.
But the defiant German rejected this idea, saying it would breach the constitutional rights of lawmakers to have the freedom to vote for any chancellor candidate they want.
The news follows her coalition’s catalogue of crises that have peaked over the course of the summer period.
CSU leader and Interior Minister Horst Seehofer brought the government to the brink of collapse with a threat to turn back migrants at the border with Austria if they had already applied for asylum elsewhere in the EU.
Mr Seehofer’s hardline on immigration has not helped his to CSU reverse a slide in support in Bavaria, the main gateway for migrants coming to Germany.
Voters in the wealthy state appear to be unimpressed with his anti-immigration rhetoric.
Those opposed to Merkel’s decision in 2015 to open Germany’s borders to some one million, mainly Muslim asylum seekers, are turning to the AfD.
Yet others are leaving the CSU for the Greens, who are projected to become the second-biggest party in Bavaria mid-October.
Seehofer, the loudest critic of Merkel’s liberal immigration policies, on Saturday ruled out giving up his post as CSU leader after the election, vowing to stay on until the end of his term next year.
Asked by the Welt am Sonntag newspaper if he would stay, he said: “Of course! I have a big project to complete.”