BEIRUT — Syrian troops reached the edge of the northern province of Raqqa on Saturday, home to the de facto capital of the Islamic State group’s self-styled caliphate, in a push that leaves the extremists fighting fierce battles on four fronts in Syria and neighboring Iraq.

The Islamic State, which controls large swaths of territory in both countries, is fighting Syrian troops, US-backed fighters, and opposition militants in northern Syria and is facing an offensive by Iraqi government forces on their stronghold of Fallujah.

The Syrian government has had no presence in Raqqa since August 2014, when the Islamic State captured the Tabqa air base and killed scores of government soldiers. The provincial capital, Raqqa, became the militants’ first city.

The Britain-based Syrian Observatory for Human Rights said Syrian troops reached the ‘‘administrative border’’ of Raqqa province under the cover of Russian airstrikes. It said that during three days of fighting 26 Islamic State fighters and nine troops and pro-government gunmen were killed.

The media arm of Lebanon’s Hezbollah group, which is fighting alongside government forces, said Syrian troops reached the border of Raqqa province after advancing about 4 miles on Saturday afternoon.

The front line is around 50 miles from the city of Raqqa.

Syrian troops began their advance toward the province Wednesday, the same day that US-backed forces launched an attack on the Islamic State stronghold of Manbij, some 72 miles to the northwest of Raqqa. It is unclear whether the attacks were coordinated.

The US-backed predominantly Kurdish Syria Democratic Forces advanced closer to Manbij, which lies on a key supply route linking the Turkish border to the city of Raqqa, Saturday.

The Observatory said SDF fighters had captured 34 villages near Manbij. Another activist group, the Local Coordination Committees, said the fighting is now concentrated on the south of the town.

Islamic State fighters are also engaged in fierce battles for the rebel-held stronghold of Marea, a town some 70 kilometers west of Manbij. The Islamic State has surrounded Marea on three sides but has failed to capture the city, which is under control of rebels and fighters from the Al Qaeda affiliated Nusra Front.

‘‘The fighting is very intense on three fronts in Marea,’’ said opposition activist Baraa al-Halaby, who is based in northern Syria.

While battles rage in Raqqa province, Manbij, and Marea, Islamic State fighters are also coming under fire in their Iraqi stronghold of Fallujah. Iraqi forces launched their offensive on the city almost two weeks ago, and say they have reached the edge of town.

On the city’s northern edge, Iraq’s military issued a statement announcing that the Islamic State had been pushed out of the neighborhood of Saqlawiya on Saturday. The statement also said an Iraqi flag had been raised above the area.

However the main push into the city center has been slow. Heavy Islamic State counterattacks and concerns for the tens of thousands of civilians trapped inside the city have slowed Iraq’s counterterrorism troops, who are leading the push, according to Iraqi Prime Minister Haider al-Abadi.

Meanwhile, violence in and around the contested northern city of Aleppo, Syria’s largest city and once the country’s commercial center, claimed more lives Saturday. The city has been the scene of fierce fighting, even during a truce brokered by the United States and Russia that went into effect in late February and collapsed weeks later.

The Russian military’s Reconciliation Center in Syria said in a statement that the Nusra Front heavily shelled several government-held neighborhoods of the city.

Syrian state TV said the shelling of government-held parts of contested Aleppo killed 22 and wounded 23 people, while opposition activists said dozens were killed or wounded in rebel-held neighborhoods.

Intense fighting also took place south of Aleppo, where insurgents led by the Nusra Front attacked Syrian army position, according to the Observatory and the activist, Halaby.

‘‘The aim of the attack south of Aleppo is to reduce pressure on the city’’ by government forces, Halaby said.