According to the newspaper Augsburger Allgemeine, Bavaria's Christian Social Union (CSU) party could leave their parliamentary bloc with Angela Merkel's Christian Democratic Union (CDU) after the German chancellor failed to find a compromise with her allies on migration policy.
Despite tensions over Trump's intended trade tariffs the USA and its G7 allies had put on an apparent show of unity at the end of the tense summit.
"We finished the meeting, really, everybody was happy, and I agreed to sign something", Mr Trump told reporters at a news conference following his summit with North Korean leader Kim Jong Un in Singapore.
Asked about Trump's tweets and the future of the G7 Trudeau refused to respond directly but later issued his own tweet saying "We are focused on everything we accomplished here at the G7 summit".
President Trump is downplaying the media's reaction to the viral photo of the G-7 summit that showed him surrounded by other leaders. A White House adviser later admitted that Trump's desire to appear strong was partly the reason for this move.
It also said it supported Merkel in her initiative to allow for the return of migrants who had already applied for asylum elsewhere "in agreement with the countries most strongly affected by migration pressure within the context of the European Council".
"He learned", Mr Trump said.
"We won't let ourselves be ripped off again and again", Merkel said. But Trudeau had simply reiterated points he'd made before: that Canada planned dollar-for-dollar retaliatory tariffs in response to Trump's new tariffs on imported steel and aluminum.
German Chancellor Angela Merkel delivered a long-awaited answer to French President Emmanuel Macron's call for ambitious European Union reforms on Sunday (3 June), offering olive branches on investment and help for debt-mired eurozone member states.
However, Merkel said it is too early to give up entirely on the United States and "There are still good reasons to continue our fight [aimed at keeping a close transatlantic partnership], even though we can not just rely on it anymore".
Canadian Prime Minister Justin Trudeau's take was released with a wider frame, making sure the host, absent from most other images, was visible.
Many saw a distillation of a crisis of the West in the photograph, and a revival of the debate launched by United States and British media after Trump's 2016 election whether Merkel was the new "leader of the free world". Trump called him "very dishonest and weak" in a tweet after Trudeau repeated criticisms of USA tariffs on imported steel and aluminum and Trump's trade policies in a news conference following the Group of Seven meeting in Quebec.
Austria, a major transit nation on the migrants' route, and Italy rejected the argument this week, however, saying they supported Mr. Seehofer's initiative. "Other states will surely follow", he said in a statement.
"We spent two days producing a statement and commitments", the statement said.