On the campaign trail, no foreign policy issue seized Donald Trump more than the fight against the Islamic State. Once president, he signed an executive order giving his generals 30 days to produce a plan to defeat the terrorist group, and Defense Secretary Jim Mattis gave him options on Feb. 27.

Yet if Mr. Trump has decided on a new plan for defeating ISIS, it isn’t obvious. The missions underway in Iraq and Syria were set in motion by President Barack Obama. While they have achieved some tactical successes, they point to a deepening American military involvement in both countries. The question now is whether Mr. Trump will continue, or accelerate, that trend.

Last week, American officials announced plans to nearly double their forces in Syria with 400 more troops and the Pentagon is reportedly considering sending 1,000 extra troops to Kuwait as a reserve force. They are also weighing more troops for Iraq, where about 5,000 Americans are training and assisting Iraqi security forces. Though the Americans are not expected to be involved in ground combat, they are moving closer to the front lines.

As a candidate, Mr. Trump derided Mr. Obama’s anti-ISIS strategy as a disaster, though offering none of his own. Now, in office, he shouldn’t ignore the progress that has been made. Local forces backed by American airstrikes have retaken large areas of Syria and Iraq that ISIS captured in 2014. The eastern part of Mosul, once Iraq’s second-largest city, was recently liberated from ISIS. On Feb. 19, Iraqi forces launched a battle for the western part of the city, where a million people are trapped in desperate conditions. Last week, an American-backed militia in Syria captured the main road connecting Raqqa to territory the group holds in Deir al-Zour Province, severing the last supply and escape route for its fighters. The group’s claim to legitimacy has rested mainly on holding territory, so losing those strongholds would be a devastating blow.