Since then, U.S. military and civilian officials in Washington have debated whether to leave some troops in Syria for a number of reasons, primarily to serve as a counterweight to Iran.

Mr. Trump’s national security adviser, John Bolton, has expressed a preference for keeping some forces in Syria, according to a former senior administration official.

Mr. Trump said earlier this month that he wants to have U.S. troops in Iraq to “keep an eye” on Iran, infuriating many Iraqi politicians who said American troops are in Iraq to support the Iraq’s fight against Islamic State, not to counter Iran. Meanwhile, multiple officials said discussions have intensified within the White House over leaving some of the troops in Syria. Leaving some troops in Syria would be a significant reversal for Mr. Trump, who has moved to bring troops home from conflicts.

The White House didn’t immediately respond to a request for comment.

U.S. troops have been in Syria primarily to flight Islamic State, but officials have said they also send an important signal to Iran. Top U.S. military officials, including Gen. Votel, say now there is value to leaving some troops in Syria to prevent groups aligned with Russia, Iran, the Syrian regime and others from filling the void.

Gen. Votel said he hadn’t made a formal recommendation, but said a decision point is fast approaching as the departure of U.S. forces and their equipment soon becomes “unambiguous.”

“There is ongoing planning, our diplomats will have to be involved in this, but certainly, this indirect advantage that we get would be beneficial to retain,” he said in an interview, referring to having troops remain in Syria to counter Iran.

Keeping some forces in Syria also would allow the U.S. to better maintain its relationship with Kurdish forces, whose control of terrain in northern Syria has had an “indirect impact” on Iran, he said.

“Having partners on the ground that we can have a relationship with and who share some of our same concerns, I think that’s a good thing,” said Gen. Votel.

If Mr. Trump were to leave some troops in Syria, it would be a sign that he had changed course on the advice of his advisors to send a message to Iran, said Jennifer Cafarella, a Syria expert at the Institute for the Study of War in Washington, D.C. Mr. Trump would also have to decide that he has other interests in Syria, such as pushing back on Russian influences inside the country. “You can’t contain Iran in Syria without also dealing with the Russians,” she said.

Military officials have indicated that the last troops to leave under the current plan likely would depart from a base known as al-Tanf, in eastern Syria near the borders of Iraq and Jordan. If a decision is made to keep troops in Syria, a contingent most likely would remain at al-Tanf, officials have said.

Fighting against Islamic State has continued in a small area in northern Syria to the east of the Euphrates River valley. This week, Kurdish forces encountered Islamic State fighters in the presence of civilians, slowing combat as U.S.-backed units tried to avoid civilian casualties, U.S. military officials said.

“It has been hard fighting, many civilians are in the area, [improvised explosive devices], and it makes for a hard fight and slow progress,” said a military official.

As the effort to retake all Islamic State territory in Syria nears completion, attention has begun to focus on the impact of the American troop departure both on the region itself and on U.S. policy regarding Iran.

Gen. Votel said Tehran continues to ship “lethal technologies” to proxies in the region, including Houthi insurgents fighting in Yemen and Hezbollah militants in Syria and Lebanon.

“I think it does pose a threat to us, and I think we have to be concerned about it,” he said.

—Vivian Salama contributed to this article.

Write to Gordon Lubold at Gordon.Lubold@wsj.com