Mr. Obama began laying the groundwork on Friday in a phone call with President Petro O. Poroshenko of Ukraine, in which the White House said he had reaffirmed American support and spoken of his determination to “maintain costs on Russia and the separatists” in eastern Ukraine until they honor a cease-fire agreement that is threatening to collapse after renewed clashes last week.

The debate over how to address Moscow’s aggression in Ukraine is likely to overshadow the meetings, to be held at a castlelike luxury hotel with sweeping alpine views.

World leaders will also weigh their next moves in the increasingly grim fight against the Sunni militant group Islamic State, after a conference last week in Paris yielded no breakthroughs on how the United States-led international coalition could reverse the group’s gains.

Mr. Obama is scheduled on Monday to meet with Prime Minister Haider al-Abadi of Iraq on the sidelines of the Group of 7 meeting. There, he is likely to hear pleas for more American help in fighting the Islamic State, whose recent gains in Iraq and Syria have left the president and coalition partners in search of a winning strategy.

It was not supposed to be this way for Mr. Obama, who, in the seventh year of his presidency, would like to use the Group of 7 gathering to advance his legacy. The president is hoping to secure pledges from American allies that they will make binding commitments to reduce their greenhouse gas emissions before a December climate change summit meeting in Paris, which he has made a top priority.

Mr. Obama also wants a strong statement from the group in support of free trade, another priority that is increasingly generating opposition both in the United States and among allies. He will need to reassure allies that even in the face of those challenges, he will ultimately have enough votes in Congress to push through trade promotion authority legislation that would pave the way for completing the Trans-Pacific Partnership, a massive deal spanning the Pacific Rim. The Group of 7 countries are more focused on a trans-Atlantic agreement, also far from being finished.

“They’ll want private assurances from the president that he’s got the votes,” said Patrick Cronin, the senior director of the Asia-Pacific Security Program at the Center for a New American Security, a Washington-based research organization.