German Chancellor Angela Merkel says she will hold talks with other European countries on migration issues and report back to her party on July 1.
Italy and France have also become involved in the migrant debate, with Italy's interior minister Matteo Salvini, who is the deputy Prime Minister of the country, refusing to accept new refugee boats and calling for asylum seekers to be equally distributed across the European Union, rather than being hosted by the first country they land in.
German Chancellor Angela Merkel dismissed claims by U.S. President Donald Trump that officials in her country are ignoring a rise in crime, saying Tuesday that the actual figures "speak for themselves".
Seehofer was quoted Sunday telling the Bild am Sonntag newspaper: "No one in the CSU has an interest in bringing down the chancellor. or blowing up the coalition".
Some political analysts have speculated that the CSU manufactured the showdown with Merkel in an attempt to mobilize right-wing voters ahead of critical Bavarian state elections in October.
Getting all of the EU states on board for an overhaul of asylum practices and rules is "in my view one of the most decisive issues for European unity", the Christian Democrat chancellor said. Merkel said she will have to discuss "what is important for others; I can't say today what that is".
Seehofer wants Germany to have the right to reject migrants who have already registered in another European Union state but Merkel opposes any unilateral move by him that would reverse her 2015 open-door policy and undermine her authority. "Of course, we need to do more to combat crime, but those were indeed encouraging numbers".
"Ms. Merkel is insisting that Germany abide by a pan-European solution while her partners are pressing for a German only policy response", said Boris Schlossberg, managing director of FX strategy at BK Asset Management. "But we stand by our position that, if this does not succeed, turning people back immediately at the border must be possible".
The meeting came after months of back-channel discussions in which both sides tried to close the gap between their divergent visions for the European Union and the Eurozone, with both leaders making some concessions to the other.
A populist-far right government in place in Italy, as well as the conservative-far right in power in neighbouring Austria, have also taken an uncompromising stance on immigration.
On Monday, Trump tweeted that crime in Germany "is way up" as he assailed what he called a "big mistake" by Europe "in allowing millions of people in who have so strongly and violently changed their culture!"
Seehofer's ultimatum has become one of the biggest challenges to Merkel's authority since she took power almost 13 years ago. About 700,000 people sought asylum in EU countries past year, down 44 per cent from 2016, according to figures released Monday by the European Asylum Support Agency.
Mrs Merkel is in the middle of a serious domestic row after defending her country's immigration policy.