Turkish troops entered central Ras al-Ayn according to Turkey's Defense Ministry, marking the most significant gain since the invasion began Wednesday. The ministry tweeted: "Ras al-Ayn's residential center has been taken under control through the successful operations in the east of Euphrates" river.
An Associated Press journalist across the border heard the sound of sporadic clashes as Turkish howitzers struck the town and Turkish jets screeched overhead.
Syrian Kurdish forces appeared to be holding out in some areas of the town.
The Kurdish Syrian Democratic Forces released two videos said to be from inside Ras al-Ayn, showing fighters saying that it is Saturday and they are still there.
The fighting was ongoing as the Kurdish fighters sought to reverse the Turkish advance into Ras Al-Ayn, the Syrian Observatory for Human Rights said.
The push deeper into northern Syria by Turkish troops came days after U.S. President Donald Trump cleared the way for Turkey's air and ground invasion, pulling back U.S. forces from the area and saying he wanted to stop getting involved with "endless wars."
Trump's decision drew swift bipartisan criticism that he was endangering regional stability and risking the lives of Syrian Kurdish allies who brought down the Islamic State group in Syria. The Kurdish-led Syrian Democratic Forces was the main U.S. ally in the fight against the Islamic State group and had lost 11,000 fighters in the nearly five-year battle against the extremists.
Earlier in the day, Turkish troops moved to seize control of key highways in northeastern Syria, the Turkish military and the Observatory said.
Turkey's state-run Anadolu news agency said that Turkey-backed Syrian opposition forces had taken control of the M-4 highway that connects the towns of Manbij and Qamishli.
The SDF said that Turkish troops and their Syrian allies reached the highway briefly before being pushed back again.
Turkish troops also cut the route linking the northeastern city of Hassakeh with Aleppo, Syria's largest city and once commercial center, according to the Observatory.
Since Wednesday, Turkish troops and Syrian opposition fighters backed by Ankara have been advancing under the cover of airstrikes and artillery shelling, reaching the Manbij-Qamishli road about 30 kilometers (19 miles) south of the Turkish border.
Turkey has said it aims to push back the Syrian Kurdish People's Protection Units, or YPG, which it considers terrorists for its links to a decades-long Kurdish insurgency within its own borders. The YPG is a main component of the SDF.
The U.N. estimated the number of displaced at 100,000 since Wednesday, saying that markets, schools and clinics also were closed. Aid agencies have warned of a humanitarian crisis, with nearly a half-million people at risk in northeastern Syria.
Turkish President Recep Tayyip Erdogan said Friday Turkey won't stop until the Syrian Kurdish forces withdraw below a 32 kilometer (20 miles) deep line from the border.
The Turkish military aims to clear Syrian border towns of Kurdish fighters' presence, saying they are a national security threat.
A civilian wounded in a mortar strike from Syria the previous day in the Turkish border town of Suruc died, Anadolu news agency also reported Saturday, bringing the civilian death toll to 18 in Turkey. Turkey's interior minister said hundreds of mortars, fired from Syria, have landed in Turkish border towns.
The Observatory that keeps track of Syria's civil war said 74 Kurdish-led SDF fighters have been killed since Wednesday as well as 49 Syrian opposition fighters backed by Tukey in addition to 21 civilians on the Syrian side.
Turkey's defense ministry said it "neutralized" 415 Syrian Kurdish fighters. The number could not be independently verified. Four Turkish soldiers have been killed since the beginning of the offensive, including two who were killed in Syria's northwest.
France's leader warned Trump in a phone call that Turkey's military action in northern Syria could lead to a resurgence of Islamic State activity.
President Emmanuel Macron "reiterated the need to make the Turkish offensive stop immediately," his office said in a statement Saturday.