Seehofer's main demand is that asylum seekers should be turned back at the German border if it is established that they entered the European Union in another country or if they have already applied for asylum in Germany and had their applications turned down.
The announcement by Kurz in Berlin after talks with German Interior Minister Horst Seehofer marks a shot across the bow at Chancellor Angela Merkel, who is trying to pull together a deal for European Union cooperation on placing asylum seekers.
It is also highly unusual for bilateral meetings to take place between government members of differing ranks, such as a leader and an interior minister, and the much-publicised episode contributed to making Merkel look increasingly isolated.
Merkel said she expected Italy's new coalition government to vote for the extension of European sanctions against Russian Federation. That has been postponed, but Merkel's Christian Democrats (CDU) and Seehofer's Christian Social Union (CSU) hope to find a compromise on the plan this week, Seehofer said.
On that last point at least, the two leaders saw eye to eye, with Kurz saying he wanted to beef up the EU's border force Frontex and give it more powers to "reduce the number of arrivals".
"We won't let ourselves be ripped off again and again", she said, referring to the new American tariffs on imported steel and aluminum.
However, a new anti-establishment Italian government is also vowing to turn away migrants - it has already forced one ship to divert to Spain - and it is unclear whether she will succeed.
Seehofer takes a much harder line than Merkel on immigration and was expected to present a "migration master plan" this week.
Austria, a major transit nation on the migrants' route, and Italy rejected the argument this week, however, saying they supported Mr. Seehofer's initiative.
"We must decide who comes to Europe, not the smugglers", said Kurz, who is due to meet with Seehofer on Wednesday. "Slowly but surely, the realization is dawning on Europe that a European solution for the asylum crisis doesn't work", said one of the party's leaders, Alexander Gauland.
Seehofer also won support from Italy's far-right Interior Minister Matteo Salvini, who on Monday flatly refused to allow a rescue vessel carrying hundreds of migrants to dock.