WASHINGTON — A new military strategy to meet President Donald Trump’s demand to “obliterate” the Islamic State group is likely to deepen U.S. military involvement in Syria, possibly with more ground troops, even as the current U.S. approach in Iraq appears to be working and will require fewer changes.

Details are sketchy. But recommendations due at the White House on Monday are likely to increase emphasis on nonmilitary elements of the campaign already underway, such as efforts to squeeze IS finances, limit the group’s recruiting and counter IS propaganda that is credited with inspiring recent violence in the U.S. and Europe. One official with knowledge of the recommendations said the report would present a broad overview of options as a starting point for a more detailed internal discussion. The official wasn’t authorized to speak to reporters about the contents of the document and demanded anonymity

Marine Corps Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, said Thursday that the emerging strategy will take aim not just at the Islamic State militants but at al-Qaida and other extremist organizations in the Middle East and beyond, whose goal is to attack the United States. He emphasized that it would not rest mainly on military might.

“This is a political-military plan,” he said. “It is not a military plan.”

Dunford’s comment suggests that Pentagon leaders have a more nuanced view of the IS problem than is reflected in Trump’s promise to “obliterate” the group, as he put it on Friday.  Dunford said the U.S. should be careful that in solving the IS problem it does not create others, hinting at the sensitive question of how to deal with Turkey, which is a NATO ally with much at stake in neighboring Syria, and Russia, whose military action in Syria has had the effect of propping up the Syrian regime.