According to several reports, Interior Minister Horst Seehofer suggested he would give Merkel two weeks to reach an agreement on the issue with Germany's European Union partners. Merkel, however, opposes any unilateral move to reverse her 2015 open-door policy and undermine her authority.
Merkel's Christian Democrats and their Bavarian sister party, the Christian Social Union (CSU), are embroiled in their own dispute over immigration that has threatened to break apart her coalition government.
NELSON: The interior minister and his party, which is facing a major challenge from far-right populists in upcoming regional elections, say they will unilaterally prevent migrants from crossing Bavaria's global borders if Berlin doesn't act. That banished - if only for now - the specter of Seehofer pushing through his proposal in defiance of the chancellor, which would risk bringing down her government.
While Merkel would welcome a reprieve from an immediate crisis in her coalition, she is still under intense pressure to deliver a deal with European Union partners who are deeply divided.
Migration "is a European challenge that needs a European answer", she said in her weekly video message Saturday.More news: Time magazine's latest cover shows Trump staring down viral immigrant girl
Mr Schmieding said: "She will need a bit of a compromise here and there".
It wasn't immediately clear what she might offer other countries in the talks. "Today there is a real choice of society, even civilisation that is up for discussion".
Merkel's talks on Monday evening with Italian Prime Minister Giuseppe Conte could prove crucial if she is to have any chance of finding concordance in Brussels.
"There are two or three remaining issues" to sort out, a European source close to the negotiations said. She also called for doing more to stop human smugglers. We must always do more to fight criminiality.
"We wish the chancellor success in this", he said.
"An important part of the masterplan is the possibility of turning people back at the border", Soeder told reporters ahead of the meeting in Munich.More news: Jay-Z, Beyonce Release Surprise Album 'Everything Is Love'
Seehofer said he told fellow leaders that "we're not out of the woods yet".
However it ends, the spat has laid bare the limits of Merkel's authority in a fractious government that took office in March after almost six months of postelection haggling. A regional party in her ruling coalition is demanding tighter rules for migrants entering the country, and that party vows to act unilaterally if the chancellor refuses. But pointedly, Kurz announced the plan with Seehofer, not Merkel, standing by his side.
Most first arrived in Bavaria, which borders Austria.
President Trump is digging in on a demonstrably false claim that the crime rate in Germany has risen as a result of refugees in that country, despite the fact that the government of Germany recently released data showing the exact opposite - that the crime rate has actually decreased in Germany to the lowest levels since 1992.
The reference to the summit is significant; Merkel has indicated she plans to push her fellow European leaders for a new approach to asylum when they meet late next week. Around 30 percent came from conflict-torn countries such as Syria and Iraq.More news: Government defeated heavily in Lords on 'meaningful' Brexit vote