Seehofer has been calling for Germany to turn back migrants previously registered as asylum-seekers in other European countries.
Merkel said she would hold bilateral agreement talks during a June 28-29 European Union summit.
"We want to make sure that we don't always wait for absolute consensus", she said, and argued that such changes have become necessary to better respond to an ever changing world.
"Asylum-seekers who have been registered in other European Union member states should be turned away at Germany's border", he insisted, despite Merkel's opposition to such a unilateral step. As she so often does with the men who challenge her, Merkel gave him just enough rope to hang himself.
As outspoken pro-Europeans, Merkel and Macron both face harsh opposition from nationalist and right-wing populist forces at home, and in the governments of Italy, Austria and several eastern European countries. Merkel isn't against a stricter border regime, but wants this to be part of a European agreement, which she hopes to achieve at an EU summit at the end of this month. Without the CSU, Merkel's coalition, which also includes the Social Democrats, would lose its parliamentary majority.
Seehofer insisted on his right in the absence of a European deal to order police in Bavaria to start turning away migrants by next month if Merkel fails to find solutions with EU partners.More news: Official Google Podcasts app now available in the Play Store
Macron said it would be operational by 2021, but their plans lacked further detail.
Later in the day, she will host the new Italian Prime Minister, Giuseppe Conte, who is heading a government with an anti-immigration agenda.
In Germany, the question of how the country should handle migrants has pushed Merkel's governing coalition to the brink of collapse. Or if they had already applied for asylum and been rejected.
In his previous job as Bavarian governor, Seehofer was one of the leading critics of Merkel's decision in 2015 to leave Germany's borders open as migrants streamed across the Balkans.
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.
Now, however, Italy's new anti-establishment government has demanded that Europe does more to help it handle refugees and migrants arriving from across the Mediterranean.
The office said 728,470 application requests were made for worldwide protection in 2017, compared to nearly 1.3 million applications the previous year.