The survey, commissioned by Die Welt, found 46 percent of respondents want the embattled Chancellor to step down before talks on forming a new government get under way early next month.
A further 17 percent believe Mrs Merkel should quit if talks over a coalition agreement between her Christian Democratic Union (CDU) and Christian Social Union (CSU) bloc and the centre-left Social Democrats break down.
A survey published by Bild earlier this week showed that 47 percent of those asked would like Merkel to leave office before completing a fourth term in 2021.
The results of the Die Welt poll — taken from 5,120 respondents surveyed between December 28 and 30 — also show that supporters of the far-right Alternative for Germany party are keenest to see Mrs Merkel to go, with 87 per cent saying she should step down immediately.
Talks exploring a possible deal between the SPD and CDU/CSU will start on January 7.
Previous three-way talks between the CDU/CSU, Greens and liberal Free Democratic Party (FDP) broke down in November.
Mrs Merkel’s conservatives won national election in September with a reduced majority but her failure to create a working coalition have led to growing calls for her to step down.
Her dwindling popularity following her handling of the recent migrant crisis in Europe has opened up divisions within her own party and Jens Spahn has emerged as a potential challenger.
The FDP’s Bundestag vice leader Michael Theurer ruled out the possibility of a government alliance with the FDP while Mrs Merkel is still in control.
He told Bild: “The Union must have the courage to include new faces: Jens Spahn instead of Angela Merkel – that would work for us as the FDP!
“With all successes and her international reputation, Mrs Merkel stands for yesterday’s battles.
“Mrs Merkel has her merits: especially in foreign policy, and to some extend in managing the financial crisis.
“But being just a crisis-chancellor is not enough. Modernisation is needed.
“Obviously she does not have the strength anymore.”
Mr Theurer accused Mrs Merkel of “backroom politics”, “lulling rituals” and a deliberate “asymmetric demobilisation” of voters as he proposed reducing the length of time a German Chancellor can remain in power.
He said: “We should seriously think in Germany about a term limit for the Federal Chancellor. Konrad Adenauer’s was two years too long, Helmut Kohl’s as well. And it seems similar with Mrs Merkel.
“In the US and France, the heads of government are allowed a maximum of two consecutive terms.
“These two mother countries of democracy have their reasons for this. Democracy needs the change. Otherwise it will be stuck.”