Iran is expanding its already sizable role in Syria’s multisided war in the wake of Russia’s airstrikes, despite the risk of antagonizing the U.S. and its Persian Gulf allies who want to push aside President Bashar al-Assad.

Politicians in the region close to Tehran as well as analysts who have been closely following its role in Syria say a decision has been made, in close coordination with the Russians and the Assad regime, to increase the number of fighters on the ground through Iran’s network of local and foreign proxies.

The support also could involve more Iranian commanders, military advisers and expert fighters usually assigned to these units, these people said.

Russian warplanes ventured into Raqqa, the home base of Islamic State extremists, for the first time as they flew more than a dozen sorties Friday, the third day of airstrikes. The Russian Defense Ministry said they had destroyed command centers, weapons stores and a communication hub.

Russian planes also pounded areas controlled by other rebel factions that threaten Mr. Assad’s coastal strongholds.

President Barack Obama sharply criticized Russian President Vladimir Putin’s military approach in Syria and warned that he risks getting stuck in a quagmire of sectarian violence if he doesn’t focus on defeating Islamic State and help broker a deal for Mr. Assad to leave power.

U.S. officials said Mr. Obama’s advisers are debating possible changes to their strategy, including sending more arms to opposition forces and setting up safe zones for refugees and opposition fighters.

Even more than Russia, Iran has long been Mr. Assad’s main backer, providing him with financial and military lifelines as he has battled rebel groups and Islamic State, the Sunni Muslim extremist group. The U.S. and its allies, including Saudi Arabia, Qatar and the United Arab Emirates, want to push Mr. Assad aside.

Wiam Wahhab, a former Lebanese minister allied to Iran and Mr. Assad, stressed that Iran wouldn’t be dispatching troops in the conventional sense. Instead, they were likely to be officers and advisers from the Islamic Revolutionary Guard Corps, or IRGC, he said.

“I know there is a major battle upon us and everything needed for this battle will be made available,” said Mr. Wahhab, who has some members from his own political party fighting in Syria alongside the regime. “There is a plan to carry out offensive operations in more than one spot.”

Experts believe Iran has some 7,000 IRGC members and Iranian paramilitary volunteers operating in Syria already.

Separate from the regular army, the IRGC was founded in the aftermath of the 1979 revolution as an ideological “people’s army” reporting directly to the supreme leader, Iran’s top decision maker.

The more than 100,000-strong force controls a vast military, economic and security power structure in Iran and is in charge of proxies across the region. Its paramilitary organization, the Basij, was the lead force in the crackdown on pro-democracy demonstrators in 2009.

Since late 2012 Iran has played a lead role in organizing, training and funding local pro-regime militias in Syria, many of them members of Mr. Assad’s Alawite minority, a branch of Shiite Islam. Experts believe they number between 150,000 and 190,000—possibly more than what remains of Syria’s conventional army.

What’s more, some experts estimate 20,000 Shiite foreign fighters are on the ground, backed by both Shiite Iran and its main proxy in the region, the Lebanese Shiite militia Hezbollah.

About 5,000 of them are new arrivals from Iraq in July and August alone, said Phillip Smyth, a researcher at the University of Maryland. He said this figure was compiled through his own contacts with some of these fighters, flight data between Baghdad and Damascus as well as social media postings. “It looks like it was timed out to coincide with the Russian move,” Mr. Smyth said.

Late last month, the Iraqi militia called Katai’b al-Imam Ali posted videos of its fighters in Syria. Analysts at the Washington-based Institute for the Study of War said Friday they “are likely conducting the ground offensives in Syria supporting Russia’s airstrikes.”

Katai’b is directly supported by the IRGC.

Mr. Smyth said he has also tracked an increase in the number of Pakistani Shiite fighters going to Syria this year, and that many of them are coming through the Iraqi networks. He also said the flow of Afghan Shiite fighters, which began in late 2013, has been steady.

“They are all agents of the Islamic Revolution, their nation states do not matter,” he said. “They will all be clumped together on major fronts and in battles where needed.”

He said an increase in both local and foreign militias overseen by Iran will undoubtedly mean more Iranian expert fighters and commanders assigned to them on the front lines. “Since 2013 they have engaged in a more direct combat role on the ground as opposed to simply functioning as advisers and commanders,” he said.

Some rebel leaders and opposition activists say they have already detected in conjunction with the Russian airstrikes a buildup in both local and foreign militias backed by Iran in areas in Hama and Homs provinces, two places crucial for shoring up the defenses of regime strongholds along the coast.

Marziyeh Afkham, an Iranian foreign-ministry spokeswoman, said Thursday that Iran supported the Russian strikes, and urged “a joint international move” to fight terrorism in the country, according to comments carried by Iran’s official state news agency. She didn’t elaborate.

Theodore Karasik, a senior adviser at Gulf State Analytics in Dubai, said a robust deployment of Iranian-backed forces could help the Syrian army clean up pockets of resistance, acting as “the fist” on the ground “to Russia’s air campaign from above.”

An Iranian diplomat on Friday told Russia’s Interfax news agency that the country didn’t need to send troops to Syria and that its military aid was limited to advisers. The diplomat said Iran’s line of support on the ground went through Hezbollah, which fights alongside Mr. Assad’s forces. “Iran always supports Hezbollah, and Hezbollah now supports Syria, led by President Assad,” the unidentified diplomat was quoted as saying.

Mustafa Alani, the director of security and defense studies at the Geneva-based Gulf Research Center, said Iranian interests were focused on retaining Mr. Assad in power. “They see Mr. Assad as the only guarantor of Iranian influence and support for Hezbollah,” he said.

Washington is leading its own campaign of airstrikes against Islamic State in Syria and Iraq, but wants to see Mr. Assad removed. The U.S. is deeply suspicious of Iranian military goals in the region, including in Syria and Yemen—a wariness shared by its Sunni Muslim allies, led by Saudi Arabia.

Despite ideological differences between Syria’s secular Baath Party regime and Iran’s Islamic government, the countries have been allies since Iran’s revolution in 1979.

Syria, at first the dominant power in the relationship, supported Iran in the Iran-Iraq War of the 1980s and became a primary conduit for Iranian aid for other Shiite groups in the region, including Hezbollah in Lebanon.

In the aftermath of the Arab Spring in 2011, Iran became the dominant partner. A U.N. official this year valued Iran’s aid to Syria at billions of dollars annually, a sum that has helped support local militias dominated by Alawites.