Horst Seehofer has been at odds with the chancellor over her approach to mass migration.
He has threatened to turn away some categories of asylum seekers at the German border while Mrs Merkel has sought a European solution.
Sources in Mr Seehofer’s party – Bavaria’s Christian Social Union (CSU) – said he wanted to step down as interior minister and chairman of his party, as he enjoys no support.
The CSU tried for weeks to get Mrs Merkel to agree to reject asylum seekers at the border if they had already registered in other countries or to get a similar deal from the European Union by 1 July.
Mr Seehofer complained in Sunday’s closed meeting with party bosses that his conversation with the chancellor had no effect, sources said.
Germany’s DPA news agency reported that some members of Mr Seehofer’s party were trying to change his mind on the resignation.
It is not clear what effect Mr Seehofer’s resignation could have on Mrs Merkel’s government, which has looked increasingly precarious during the three-week stand-off.
The CSU and Mrs Merkel’s CDU (Christian Democratic Union) have been allies since 1949 but the CSU faces a state election in Bavaria in October, and its anti-immigration stance is its main campaign platform.
News Source SkyNews