KRÜN, Germany—President Barack Obama and other world leaders laid the groundwork for more strenuous action against Russian aggression and in the battle with Islamic State militants, raising the specter of fresh sanctions against Moscow and signaling plans to accelerate training for Iraqi forces.

After a summit in Germany with leaders of the world’s largest industrialized democracies, Mr. Obama acknowledged challenges that the U.S. and its allies face in two of the world’s most pressing foreign-policy crises.

While leaders of the Group of Seven nations claimed agreement on key global issues such as climate change, they found few easy answers in a two-day summit to conflicts in Ukraine and the Middle East.

Mr. Obama said after a meeting at the summit with Iraqi Prime Minister Haider al-Abadi, that the Pentagon is working on a plan to speed up the training and equipping of the Iraqi military, but that he needed commitments from Iraqi officials to step up training and recruiting.

In the absence of such pledges, the U.S. hasn’t yet developed a “complete strategy” for training the Iraqi military, Mr. Obama said. The Pentagon is assessing strategies to hasten progress, but the details haven’t been settled, the president said Monday during a news conference at the conclusion of the G-7 summit in the Bavarian Alps.

“When a finalized plan is presented to me by the Pentagon, then I will share it with the American people,” Mr. Obama said.

Despite recent setbacks in the fight against Islamic State and persistent questions about the strength of the Iraqi military, the president said the U.S. has made significant progress pushing back the extremist group in some areas.

“Where we’ve trained Iraqi forces directly and equipped them…they operate effectively,” Mr. Obama said. “Where we haven’t, morale, lack of equipment, etc., may undermine the effectiveness of Iraqi security forces.”

The president’s acknowledgment that the U.S. doesn’t yet have a complete strategy drew derision from critics and spurred comparisons to a similar comment in August, when Mr. Obama said almost a month into the airstrike campaign in Iraq that the U.S. didn’t yet have a fully formed strategy.

On Monday, Michael Short, a spokesman for the Republican National Committee, questioned the administration’s approach.

“When President Obama said 10 months ago he didn’t have a strategy to combat ISIS, it was deeply troubling, and the fact he still doesn’t have a final plan for the deteriorating situation in Iraq is unacceptable.”

State Department spokesman Jeff Rathke said that the president on Monday hadn’t been discussing the broader strategy. “He was speaking about how to accelerate and optimize the training and equipping of Iraqi forces, including the integration of Sunni fighters,” Mr. Rathke said.

The president said he told Mr. Abadi that political inclusion in recruiting Iraqi forces is as important as the fight. The U.S. has pressed the Iraqi prime minister to improve outreach to the country’s Sunni minority to help calm Iraq’s Shiite-Sunni divide.

At the Pentagon, Col. Steve Warren, the spokesman, said the Department of Defense is continuing to work on options for the White House. Last month, Defense Secretary Ash Carter asked experts in the Pentagon to develop potential plans to increase support for the Iraqi security forces.

The U.S. has trained 8,920 Iraqis at its four training sites in the country. Another 2,601 Iraqis are currently going through the training.

Addressing the Ukrainian crisis, Mr. Obama suggested Monday that Russia could face new sanctions for continuing to violate the Minsk cease-fire agreement, as U.S. and European officials have accused it of doing.

After the president spoke, the Pentagon announced Monday that U.S. and European allies have begun a large military exercise in the Baltic Sea.

The area has been the site of escalating tensions between Russia and planes flown by the U.S. and its allies. In April, U.S. officials accused Russia of conducting an unsafe intercept of an American reconnaissance plane.

The new exercise began June 5 and will involve 5,600 military personnel—including 2,000 Americans.

During their meetings in Germany, G-7 leaders discussed possible additional steps—beyond existing economic sanctions—that could be taken if Russia “doubled down on aggression inside of Ukraine,” the president said.

“Those discussions are taking place at a technical level, not yet at a political level,” Mr. Obama said. “Our hope is…that we don’t have to take additional steps.”

In a G-7 communiqué, leaders also threatened further sanctions if Russia takes more aggressive actions in eastern Ukraine. Sanctions against Russia, the leaders said, “can be rolled back” when Russia meets the Minsk commitments, the communiqué said.

German Chancellor Angela Merkel said in comments in Germany that all summit participants agreed that the path to solving the Ukraine crisis lay in following the peace plan forged in Minsk, Belarus, in February.

The Minsk plan includes measures to grant regions of eastern Ukraine more autonomy in addition to establishing a cease-fire and the withdrawal of heavy weaponry—all points that are still far from being fully implemented.

“We are of the opinion that we must do everything we can in order to move the political process of Minsk forward,” Ms. Merkel said.

What happens next is up to Russian President Vladimir Putin, Mr. Obama said.

“Does he continue to wreck his country’s economy and continue Russia’s isolation in pursuit of a wrongheaded desire to re-create the glories of the Soviet empire?” Mr. Obama said. “Or does he recognize that Russia’s greatness does not depend on violating the territorial integrity and sovereignty of other countries?”