The U.S. and Russia will meet for their first face-to-face talks on Syria since Russian warplanes began flying combat missions there at cross purposes with an American-led campaign.

U.S. Secretary of State John Kerry will meet his Russian counterpart as well as top diplomats from Saudi Arabia and Turkey on Friday in Vienna as the Obama administration grasps for a way to salvage its Middle East agenda.

The meeting follows a visit to Moscow this week by Syrian ruler Bashar al-Assad—his first known trip outside his country since the start of its conflict more than four years ago. It was a show of defiance to the West and a sign of Russia’s effort to position itself as the essential power broker in the region.

Mr. Kerry will voice U.S. concern about Russia’s airstrikes against the Assad regime’s foes and what Washington sees as a need to move toward a political transition in Syria that would remove Mr. Assad from power.

However, U.S. expectations have been tempered by Russia’s military campaign.

“The secretary is a pragmatist, here,” said John Kirby, the State Department spokesman. “He recognizes that not everybody shares that view.”

Mr. Kirby said U.S. officials weren’t surprised by Mr. Assad’s visit to Moscow, “given the relationship that Syria has with Russia, and given the recent military activities by Russia in Syria” on his behalf.

In Moscow, Russian President Vladimir Putin was shown in a video released Wednesday sitting opposite Mr. Assad in the Kremlin. Mr. Putin said the Syrian government had “achieved significantly positive results” in its fight against an array of opposition forces, and was prepared to help lead the country to a political solution to end the war. The official Syrian Arab News Agency confirmed that Mr. Assad met Mr. Putin on Tuesday at the Russian leader’s invitation, saying the two had discussed further joint operations against terrorist groups in Syria, using the Syrian government’s term for its opponents.

Russia began airstrikes in support of Mr. Assad’s forces in late September, a move that is frustrating Washington and its allies and complicating a U.S.-led coalition effort to rout extremist group Islamic State.

With its military intervention, the Kremlin positioned itself as the key player in resolving the conflict—and helped Mr. Assad avert outright defeat on the battlefield.

In the months before the bombing campaign, Syrian government forces had been losing ground through defections and casualties; now, the government in Damascus is confident enough to press an offensive to regain territory once considered out of Mr. Assad’s control.

The regime began a ground offensive around the city of Aleppo on Friday. Syrian, Iranian and Hezbollah fighters backed by Russian planes captured a string of villages over the weekend along the city’s southern outskirts, the government’s biggest advance since the Russian intervention.

On Wednesday, fighting continued as the regime tried to push westward toward a highway leading to the coast and south to the capital, Damascus. The Russian Ministry of Defense said its warplanes had flown 46 combat sorties in the previous 24 hours, attacking 83 ground targets.

The air campaign is also not the first time Moscow has come to Mr. Assad’s rescue. In September 2013, the Obama administration set aside a push toward military action against Mr. Assad after Russia declared support for a plan to allow him to hand over his chemical weapons to the international community.

In Moscow, Mr. Assad told the Mr. Putin that terrorism is impeding the path to a political solution, SANA reported, and said the military operation by the two countries must be followed by political steps.

“Everyone understands that any military action suggests further political steps,” the Syrian president said. “And of course, the common goal for us all should be what the Syrian people want to see for the future of their country.”

Mr. Putin said Russia was willing “not only to take the path of military action in the fight against terrorism, but to take the path of a political solution” to end the conflict.

The Kremlin has portrayed its military support for Mr. Assad as a bid to defeat extremists abroad before they return to Russia. The Kremlin says thousands of citizens of the former Soviet Union have made their way to Syria, where they have received indoctrination and training from Islamic State.

“It worries us as well—Russia, I mean—that unfortunately a minimum of around 4,000 people from the republics of the former Soviet Union have taken up arms against the government forces and are fighting on the territory of Syria,” Mr. Putin added.

While Russia has said it is targeting Islamic State militants, most of its airstrikes have been on mainstream rebels, some of which have been trained and equipped by Washington.

Russia’s military campaign in Syria has been carried out primarily by fighter aircraft that have conducted intensive bombing runs in support of Mr. Assad’s forces. Mr. Putin has publicly ruled out the deployment of ground troops.

The Russian military operates drones and aircraft from a Syrian air base that has been reinforced with armored troop carriers and tanks. Asiyat Turuchiyeva, a representative of the Russian embassy in Damascus, denied reports that Russian forces had sustained casualties in recent days.

Russian strikes as well as the regime’s offensives across central and northern Syria have taken a large humanitarian toll, Syrian activists say. At least 127 civilians, including 36 children and 34 women, have been killed by Russian airstrikes, according to the opposition Syrian Observatory for Human Rights.

The United Nations estimates that at least 90,000 civilians have been displaced by the fighting along numerous front lines, most of them in Aleppo and Hama provinces. Some are living with host families while others are seeking shelter in tent camps which provide little protection from the cold weather at night.

In Hama province, where the regime has been stalled by rebel defenses, Mr. Assad’s visit to Moscow was cast by rebels as a sign of weakness.

“Since the beginning of the revolution he has been a prisoner of the presidential palace, and now Bashar has sneaked away for a visit to meet Putin in Moscow and returned before they publicized the news,” said Abu al-Majid al-Homsi, a commander in Hama with Suqoor al-Ghab, a rebel group that has received CIA training.

The Moscow visit as well as the military intervention could position Russia as Syria’s closest ally and diplomatic partner, while possibly sidelining Iran. Last month, Iran helped broker a local cease-fire deal between rebels and Hezbollah and regime fighters. At the time it was seen as a sign of Iran’s growing role inside Syria and possibly the sidelining of Assad himself.

Now that cease-fire deal has been eclipsed by regime offensives on multiple fronts and Russia’s muscular intervention.

“Russia wants to take Assad out of the international isolation he is living,” said Husam Salameh, a leader with the Islamist Ahrar al-Sham, a group fighting alongside many of the U.S.-backed rebel factions.