At issue Monday was whether the CSU would give her time to try to reach such a deal.
She said she would report back July 1 on the results of her negotiations, and that as far as she's concerned it's not yet clear what will happen if there's no European deal on the divisive topic.
Merkel's welcome to refugees also infuriated Seehofer and his CSU, the sister party of her Christian Democrats in the southern state of Bavaria, which became the main entry point for most migrants. The CSU, which now has an absolute majority in the state, has come under fire from the far-right Alternative for Germany (AfD) amid the refugee influx.
Seehofer's "migration master plan", which Merkel last week refused to endorse, would see asylum seekers arriving at Germany's borders turned away if they have no identification papers, have already had an asylum claim rejected in Germany, or are already registered in another country in the EU - proposals that rights group say contravene European and worldwide agreements.
Mr Merkel is adamant that there needs to be a Europe-wide migrant policy, but Mr Seehofer disagrees and last week reportedly told CSU leaders in private he "can no longer work" with the chancellor. Merkel opposes any unilateral move by him that would reverse her 2015 open-door policy on migrants and undermine her authority. If Seehofer actually goes ahead and implements it unilaterally in defiance of Merkel, it could set off a chain of events that would bring down Germany's coalition government.
In Munich, Seehofer said his party would be happy to see European or bilateral solutions this month that "achieve the same that we can achieve by turning people back at the border".
"I believe it is worthwhile to keep CSU and CDU together".
Signalling that he is leaning towards the latter option, Seehofer wrote in a column in Frankfurter Allgemeine Zeitung that "it is essential that the European Union summit takes a decision at the end of June".
"Angela Merkel's coalition is coming under increasing strain over the migrant issue. The situation is serious but still solvable".
CSU General Secretary Markus Blume told the Straubinger Tagblatt newspaper the party stood behind Seehofer.
Such a direct challenge to Merkel would force her to fire Interior Minister Horst Seehofer - a vocal critic of her open door immigration policy and a thorn in her side.
But the rest of the European Union is now engaged in an unseemly squabble over refugees as the new anti-immigrant Italian government has drawn the ire of Prime Minister Macron of France by refusing docking rights to a refugee ship.
The chancellor, who is scheduled to meet her French counterpart Emmanuel Macron next week, said Germany and France would seek to set the agenda for European Union cooperation on defense, security and foreign policy ahead of the June summit.
It wasn't immediately clear what she might offer other countries in talks.
Merkel also said Germany and France would try to give new momentum to EU cooperation on foreign, defence and security policy and on further developing the economic and currency union.
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