"Yes, I am firmly convinced [that my party is behind me]," the Chancellor told Bild in an exclusive interview for Monday's edition.
"I'm not surprised that there are CDU members who have difficulty with this. We are the broad party of the nation, within which there have always been several currents."
Merkel added that it was her job to represent everyone in the party – not just those shouting the loudest to complain about her refugee policy.
"Polls are not my measure," she added when confronted with falling support for the CDU among voters in the latest surveys.
"My measure is the task that I have as Chancellor: to solve the problem. And I'm completely and entirely concentrated on that."
Merkel said that she would meet monthly with local government leaders to keep her finger on the pulse of the situation.
"That's how I'll learn where the need is greatest and where help is needed," she said.
No new solidarity tax
The Chancellor waved away rumours that her government had no plans to impose a tax hike to cope with a record influx of asylum seekers, firmly denying reports that Berlin and the European Commission were mulling a special refugee solidarity levy.
"Yes, affirmative," she said when asked to confirm that there would be no tax hikes over the refugee crisis, adding that Germany has "managed our budget well in the last few years and our economy is in a good shape".
The Süddeutsche Zeitung had claimed in a report Saturday that Berlin and Brussels had discussed the possibility of raising funds to cope with Europe's biggest refugee crisis through a special tax, which could take the form of higher levies on fuel or VAT.
But Berlin swiftly denied this, with government spokesman Steffen Seibert on Saturday saying: "We want neither a tax hike in Germany nor the introduction of an EU-tax."
On Sunday, a European Commission spokesman also rejected the claim, saying: "There is no such proposal currently on the table or under preparation and the Commission never comments on rumours in the press."
Responsibilities for refugees
Addressing fears from some quarters that Muslims could have a disproportionate impact on German culture, Merkel rounded out her interview by insisting that it was up to refugees to respect the law of the land in Germany – not for Germany to adapt itself to them.
"No-one must fear anything like that. German is and remains its Constitution, the social market economy, religious freedom and freedom of opinion," the Chancellor said.
"We will make it clear from the very first day to the people coming to us: there are laws and rules for living together in force here which you must obey. That's the only way Germany can be a place where they will be protected."
Concretely, Merkel said that meant that newcomers must "accept that in Germany men and women have the same rights."
"They will see that the public administration here doesn't work so that you can bribe someone and then get the desired result. I'm convinced that most of them will respect all of this and quickly learn to value it."
But Merkel acknowledged that some aspects of administration – especially deporting asylum seekers whose applications are rejected – needed a lot of improvement.
"In reality, that's unsatisfactory," she said.
"We will decide quickly on this matter and we've built four extra centres that are supposed to deal with these so-called 'old cases'."