A government spokesman said Mrs Merkel still had confidence in Thomas de Maiziere after he said Syrians would be treated differently in the future.
Her government was forced to clarify there had been no change in policy.
It has faced strong criticism over the thousands of refugees arriving.
Germany says it expects to receive at least 800,000 asylum seekers this year.
It has until now maintained an open-door policy for Syrians fleeing their country's civil war, offering a three-year residence permit and family reunification among other benefits.
But the interior minister appeared to catch the governing coalition by surprise on Friday when he announced that some Syrians should get a modified refugee status.
Instead, he said, they would get a one-year residency permit and they would be barred from bringing in family members.
Lawmakers from Mrs Merkel's Christian Democratic Union (CDU) backed the plan, but their coalition partners, the Social Democrats (SPD), rejected the proposal.
Government spokesman Steffen Seibert said on Twitter on Friday that Germany was "sticking to the practice currently in place".
Asked on Monday whether Mr de Maiziere retained the chancellor's confidence, Mr Seibert said "of course he does".
The huge influx of asylum seekers has caused political turmoil across the EU, with member states disagreeing about how to deal with the crisis.
Last week, Germany's government announced plans to speed up the repatriation of failed asylum seekers, after another coalition rift on the issue.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
German Chancellor Angela Merkel has backed her beleaguered interior minister following a row over restricting the asylum rights of refugees from Syria.