"Our forces entered the city of Raqqa from the eastern district of Al-Meshleb", SDF commander Rojda Felattold Agence France-Presse, adding that clashes were also raging on the city's northern outskirts.
"The fight for Raqqa will be long and hard", Lt. Gen. Steve Townsend, the coalition's commanding general, said in a statement. "ISIS threatens all of our nations, not just Iraq and Syria, but in our own homelands as well".
A statement said the pro-Assad forces ignored several coalition warnings.
After three years, ISIS is firmly entrenched in Raqqa.
After the military offensive, control of the city will be handed over to a local civilian governing council "who will provide security and governance", the coalition stated.
USA forces liberated the city alongside Kurdish militia groups, some of which Ankara considers terrorist organizations with links to Kurdish separatists who have long operated inside Turkey.
Last week, the Pentagon announced that it started delivering weapons to the SDF, a militia dominated by the Kurdish YPG (People's Protection Units), saying they were necessary to capture Raqqa, despite the objections of Turkey, a North Atlantic Treaty Organisation ally.
The YPG has been the main partner for the United States in its campaign against Islamic State in Syria, where the group is also being fought in separate campaigns waged by the Russian-backed Syrian government and Free Syrian Army rebel groups.
"The Syrian Elite Forces one or two hours ago entered the first quarter of Raqqa, which is al-Mishlab quarter, via the eastern front", he said.
"IRC health teams responding north of Raqqa city have treated people injured by mines as they attempted to cross the frontline".
Yesterday, the Observatory claimed an air strike had struck and killed 21 civilians as they fled the city across the Euphrates on a dinghy. That may indicate that IS "intends to use the 200,000 people still trapped in the city as human shields", the group warned.
The U.K. -based Syrian Observatory for Human Rights said the SDF moved into al-Mashlab neighborhood of Raqqa in the evening and took control of some buildings as IS fighters began to withdraw.
SDF commanders said they are closely monitoring the fate of residents.
Earlier Tuesday, state news agency SANA reported that the airstrikes by the USA -led coalition killed 12, including women and children. "We've seen reports of public executions of people who are trying to leave", Davis said. Bridges over the Euphrates were bombed and destroyed by the anti-ISIS US-led coalition over the past few months. Islamic State is also under assault from USA -backed Iraqi forces and allied militias in Mosul, Iraq's second-largest city.
The SDF had made significant territorial gains in recent months in its push toward Raqqa.
Between Monday afternoon and Tuesday afternoon, the coalition struck IS tactical units, destroyed 19 boats, 12 fighting positions, eight vehicles and a weapons store, he said.
The US last week said it had started distributing arms to the YPG to help retake Raqqa.
"It will obviously be an operation that is going to be hard going forward and there will be a lot of painstaking efforts to try to avoid civilian casualties as they more in".
It is unclear how many civilians remain in Raqqa.
The same route leading out of the city's southern districts has been used by IS fighters, it said.
Lt. Gen Steve Townsend, the coalition's commanding general, said the twin offensives in Mosul and Raqqa could deal an important blow to Islamic State recruiting.
Apple Showcases New iMac Pro Workstation at WWDC
Featuring next-generation Intel Xeon processors up to 18 cores, iMac Pro is created to handle the most demanding pro workflows. But the headline is the 21.5-inch iMac includes a 4K Display for $200 less than the previous generation.
Simona Halep strolls into French Open quarters
Ivanisevic, who won Wimbledon in 2001 and helped Marin Cilic win the US Open in 2014, joined Berdych's coaching team in August. It's obviously something that has affected large parts of Europe. "It's awesome how I won today, how I played against Carla".
Crosby has no time for Subban's games in Stanley Cup Final
Goaltender Matt Murray could not save Pittsburgh this time with all five goals allowed on 33 shots for a.848 save percentage. Problem is, the Predators are pressuring the puck at the point and following it fervently with their skilled defensemen.