Merkel, however, opposes any unilateral move to reverse her 2015 open-door policy and undermine her authority.
Merkel has said she is "favourable" to a French call to create a European Intervention Initiative of forces which could be deployed rapidly to deal with crises outside the framework of North Atlantic Treaty Organisation.
Merkel must now attempt to forge a deal by an EU summit on Thursday and Friday next week, and report back to her Christian Democratic Union on July 1.
Merkel welcomed compromise in the dispute, which has threatened to destabilise a coalition cobbled together just three months ago, and said her Christian Democrat (CDU) party would decide how to proceed after the two-week deadline elapsed.
Crime has fallen off dramatically in Germany, with the country's internal ministry reporting last month that criminal offenses in Germany totaled 5.76 million in 2017, the lowest number since 1992, leading to the lowest crime rate for the country in more than 30 years.
European stocks, and particularly the German market, have been hit once again over recent days by the possibility of political turmoil in Germany caused by disagreements within the ruling coalition over the country's migrant policy.
The CSU leadership agreed on Monday to delay until after a June 28-29 European Union summit the introduction of an entry ban for refugees who have already registered in other EU countries, allowing Merkel time to reach a multilateral deal.More news: Tyronn Lue doesn't seem too confident in LeBron James returning
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The decision sparked some opposition, most recently in the form of Interior Minister Horst Seehofer's open challenge to the policy, and a public poll showing 62 percent of Germans want to turn away asylum-seekers at the border.
Describing the migration crisis as one of the biggest challenges to the EU, Merkel said Germany and France would continue their efforts to develop a united European response to address this challenge.
If Seehofer, backed by his CSU, were to defy her by enforcing the plan on Monday, Merkel would be nearly certainly forced to fire him.
The European Commission urged this Monday to find "a solution within EU" to crisis unleashed in community club - and largely within Germany - for management of refugees. The CSU is determined to show that it's tough on migration, arguing that this is the best way to cut support for the far-right Alternative for Germany ahead of a challenging state election in Bavaria in October.
"We want more sovereignty and unity", Macron said. He said, if Merkel's negotiations on getting other countries to take back migrants don't bear fruit, he will talk with her party but "I want be able to put this into effect". During the height of the refugee crisis, Seehofer was sharply critical of Merkel's open-door policy, which involved accepting asylum seekers even after they had passed through other European Union states.
In an op-ed piece for the daily Frankfurter Allgemeine Zeitung released later Sunday, Seehofer said he "must have the right to turn back" people who aren't entitled to enter.