The Syrian Democratic Forces (SDF) "have completely surrounded and besieged the Islamic militants inside al-Raqqa city from all sides," the group said in a statement released late on Thursday.
The Kurdish-led SDF had been advancing from the city's east after they seized a major stronghold in May, and from the west and north.
"South of the Euphrates river the SDF now control all high-speed routes into Raqqa," Joe Scrocca, spokesman for the US-led coalition, told the Associated Press.
Moving toward the Euphrates from the east "would completely encircle the city and has been the SDF plan from the start", Scrocca added.
The UK-based Syrian Observatory for Human Rights, which monitors Syria through a network of activists on the ground, said the SDF had seized villages across the river, moving through the Kasret al-Faraj area.
The Observatory described it as a "strategic" advance that completes the siege around Raqqa.
"IS has no other choice now but to surrender or fight to the end," said the Observatory director, Rami Abdelrahman, using a different acronym for the group.
Hours after the advances, ISIL fighters carried out a counter-attack on SDF forces east of the city, regaining control of sections of al-Sinaa and Mashalab neighborhoods, which were captured in the early days of the offensive, Abdelrahman said. He said there were casualties on both sides.
Thursday's development comes as Iraqi forces captured the ruins of the famous and hugely symbolic al-Nuri mosque in Mosul where the Islamic State group's leader first declared the "caliphate" nearly three years ago.
Nearly three years ago to the day, Abu Bakr al-Baghdadi made the "caliphate" announcement in an audio recording, before appearing for the first time in public at the mosque days later.
The declaration ushered in a period of gruesome violence and an attempt by the group to erase borders between the neighbouring states.
Scrocca said Syrian fighters have pushed their way from different axes, isolating the city since the campaign began on June 6.
The coalition has destroyed all the bridges over the river and the Syrian fighters are in control of the two dams, which are the only crossing points remaining, he said. He estimated that 2,500 ISIL fighters remain in the city.
Tightening the noose around Raqqa, the de-facto capital of ISIL since they seized it in July 2014, is another symbolic development in the coordinated fight against the group.
It effectively seals the territory and denies the fighters an escape route to their other stronghold in Deir Az Zor, south of Raqqa.
Speaking in Baghdad, coalition spokesman Ryan Dillon said ISIL fighters have been "abandoned" by their leadership as a "steady stream" of leaders attempted to escape the city, some "successfully".
He said in the past week, the SDF have cleared nearly 20 square kilometres of territory in and around Raqqa.
The advance toward Raqqa city began last year, as Kurdish-led forces fought to clear ISIL from rural parts of the province.
Backed by air strikes from the international coalition, the Syrian fighters captured the strategic town of Tabqa in May, and seized one of Syria's major dams that lies nearby.
The battle for Raqqa began in earnest on June 6, as the fighters moved in from east, west and north of Raqqa.
The fight on the southern front began later this month. Scrocca warned that the fight for Raqqa city would be lengthy.
"There is still much fighting to be done in the city," he said.