Mohammed Zufar, a 20-year-old Uzbek, illustrates the conundrum. He came to Syria through Turkey in October to fight with Katibat al-Ghuraba, an Islamist group composed of fighters from Central Asia. Within weeks, he was on the front lines of the rebel offensive in a coalition led by Syrian rebel group Hayat Tahrir al-Sham.

He relied on Uzbek field commanders who spoke Arabic to convey orders from Syrian rebel leaders during the rapid offensive, he said. With the revolution over, he hopes to join Syria’s new army and help build a country on the precepts of Islamic rule.

“I came here for jihad and will stay even as a martyr,” Zufar said in a mix of Uzbek, Turkish and broken Arabic. He said he doesn’t want to return to face potential oppression in Uzbekistan: “I hope to stay here and settle.”

Zufar said he had participated in what he saw as a holy war. The Islamic rule he hopes to establish in Syria is exactly what many in the religiously and ethnically diverse society of 24 million people want to avoid.

The U.S., which made tough demands for Syria’s government in recent weeks, wants guarantees the foreign fighters won’t remain welcome in the new state.

“The interim authorities need to make sure that foreign terrorist fighters have no role in Syria’s government or military,” Tim Lenderking, a senior Middle East official at the State Department, said April 24.

Spokesmen for Syria’s transitional government didn’t respond to requests for comment.

After seizing Syria’s capital in December, the new rulers appointed foreigners to senior military positions, including men from Jordan, Egypt and Turkey. Ahmed al-Sharaa, Syria’s new president and leader of the victorious Hayat Tahrir al-Sham rebel group, known as HTS, has said foreign fighters who supported the revolution would be rewarded and potentially granted citizenship.

“They have experience in fighting in various countries, operating heavy weaponry, producing propaganda, and they have global networks both to recruit and to raise financing,” said Broderick McDonald, an associate fellow at the International Centre for the Study of Radicalisation, a think tank at King’s College London.

Their experience comes at too high a price in the minds of many Syrians.

Deadly ambushes on state security forces in March triggered reprisal killings that residents said were conducted by foreign fighters and other forces affiliated with the government.

The attacks occurred in a coastal area home to Syria’s Alawites, a minority group to which the Assad family, which ruled Syria with an iron fist for five decades, belonged. People at the time told The Wall Street Journal that convoys of armed men threatened residents, shot people and burned homes.

The Syrian government established a committee to investigate the attacks. A committee official said in April that dozens of people have been questioned and that the committee is examining more than 50 incidents. Sharaa in April approved a three-month extension of the committee’s work.

Sharaa was affiliated with Islamic State until he signed up with al Qaeda in 2012. He later cut those ties as well and fought against both groups. As president, he has distanced himself from Islamic extremism and said his government will represent all of Syria’s ethnic and religious communities.

Even Syrians critical of foreign fighters acknowledge it would be hard to purge them. While some fighters could drift off to take part in religious conflicts in places such as Africa, there is a risk others could turn against Syria’s leaders if the government abandons Islamist ideals or pushes them to return to countries where they could be repressed.

“It is impossible to deport all of them—there are a lot of political challenges” said Ziad Wannous, a 31-year-old dentist in Damascus who co-founded a democracy advocacy group after the fall of the Assad regime. But if some are to be granted citizenship, it should be done by an established process, not by fiat, he said.

Khalid Qaranful, a 24-year-old Syrian who was part of the rebel offensive, fought alongside foreign fighters who he said helped assure victory. Some foreign fighters have been in Syria for a decade, marrying Syrian women and sending their children to local schools.

“Some of them have opened shops and settled down,” Qaranful said. “And some learned to speak better Arabic than us.”

Abu Mareyah, a fighter from Lebanon, said he took up arms against Hezbollah there, then entered Syria in 2017 to fight the Assad regime and groups such as Hezbollah that were helping to prop it up.

“We as Sunnis felt threatened living under Hezbollah, and our brothers in Syria felt the same under Assad,” he said standing in front of the Umayyad Mosque in Damascus, a rallying point for Sunni Islamist fighters.

Foreign fighters, Abu Mareyah said, deserve recognition.

“Some traveled treacherous routes to arrive in Syria, giving up their lives abroad and spending tens of thousands of dollars to get here,” he said. “We are hoping to get citizenship. We have become part of Syrian society.”

Write to Omar Abdel-Baqui at omar.abdel-baqui@wsj.com