That would represent a reversal of Merkel's open-doors migrant policy adopted in 2015, which fuelled a rise in support for the right-wing Alternative for Germany (AfD) and caused rifts within her conservative bloc.
Trump responded on Twitter: "Based on Justin's false statements at his news conference, and the fact that Canada is charging massive Tariffs to our U.S. farmers, workers and companies, I have instructed our U.S. Reps not to endorse the Communique as we look at Tariffs on automobiles flooding the U.S. Market!"
"The withdrawal by tweet is, of course, sobering and a bit depressing", she said.
Mr Seehofer rejected claims he had snubbed Germany's leader.
"We must decide who comes to Europe, not the smugglers", said Kurz, who is due to meet with Seehofer on Wednesday.
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"Italy is going further than other states: migrants will not be accepted in the ports any more".
Another image of the same gathering however suggests a more relaxed interaction, with Merkel smiling and Trump making eye contact.
They told conservative lawmakers Tuesday they would try to negotiate a solution "in the coming days", participants who attended the meeting told AFP.
He has said he believes that his proposed measures are "necessary" to restore "order in Germany" and that he would not "publish a half-baked plan with lazy compromises".
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This year, quite a bit happened like US President Donald Trump asking for Russian Federation to be readmitted to the summit although Merkel was having none of it. Russian Federation was kicked out in 2014 because of its occupation of Crimea.
Seehofer, a former leader of the Bavarian Christian Social Union (CSU) which is facing a hard regional election in October, wants to show he is toughening up the rules in his 63-point master plan.
"We need a real European border police that can act if necessary even if it displeases one of the (EU) states with external borders".
But Ms. Merkel, heading a fractious alliance of center-right and center-left parties, has stuck to her pro-immigration discourse.
Kurz won the chancellery past year in an alliance with the far-right vowing to tackle illegal immigration, an issue that also propelled a populist alliance to power in Italy.
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The former Conservative prime minister said that while he believes the dispute is serious, that doesn't make it "lethal". Prime Minister Justin Trudeau , in a statement: "We are focused on everything we accomplished at the G7 summit ".
With Austria taking over the rotating presidency of the EU on July 1, Merkel is hoping to convince Kurz to sign up to a system of "flexible solidarity", and help put in place an effective European border police. She is also trying to persuade other European Union leaders to agree a common migrant policy at a summit this month.