The Kurds, who recaptured swathes of northeastern Syria from Islamic State with the backing of the United States, say the Turkish assault could allow the jihadist group to re-emerge.
In its first big attack since the assault began, Islamic State claimed responsibility for a deadly car bomb in Qamishli, the biggest city in the Kurdish-held area, even as the city came under heavy Turkish shelling.
Five Islamic State fighters fled a jail there, and foreign women from the group being held in a camp torched tents and attacked guards with sticks and stones, the Kurds said.
The Turkish incursion, launched after Trump withdrew U.S. troops who had been fighting alongside Kurdish forces against Islamic State, has opened a new front in the eight-year Syrian civil war and drawn fierce international criticism.
A war monitor gave a death toll approaching 100 from the first days of the assault. The United Nations said 100,000 people had fled their homes.
Fending off accusations he had abandoned the Kurds, who are loyal allies of the United States, Trump suggested Washington could mediate in the conflict. He also raised the possibility of imposing sanctions on Turkey, a NATO ally, a move demanded by Republican congressional critics of his policy.
Trump's defense secretary, Mark Esper, told a briefing that the United States had not abandoned the Kurds. U.S. officials had urged Turkey to halt the assault, Esper said, warning of "dramatic harm" to bilateral relations.
On Friday, Turkish warplanes and artillery struck around Syria's Ras al Ain, one of two border towns that have been the focus of the offensive, now in its third day.
Reuters reporters heard gunfire there from across the frontier in the Turkish town of Ceylanpinar.
Hundreds of kilometers further east along the frontier, a car bomb blew up outside a restaurant in Qamishli as the city came under fierce Turkish shelling. Kurdish authorities said the bomb killed three civilians and wounded nine. Islamic State claimed responsibility, saying it had targeted Kurdish fighters.
A convoy of 20 armored vehicles carrying Turkish-allied Syrian rebels entered Syria from Ceylanpinar. Some made victory signs, shouting "Allahu akbar" (God is greatest) and waving Syrian rebel flags as they advanced towards Ras al Ain.
Some 120 km (75 miles) to the west, Turkish howitzers resumed shelling near the town of Tel Abyad, a witness said. The Kurdish fighters called it the most intense fighting in three days of battles there.
Overnight, clashes erupted along the entire 400 km stretch of border from Ain Diwar at the Iraqi frontier to Kobani. "The whole border was on fire," said Marvan Qamishlo, a spokesman for the Kurdish-led Syrian Democratic Forces (SDF).
Turkish forces have seized nine villages near Ras al Ain and Tel Abyad, said Rami Abdulrahman, director of the Syrian Observatory for Human Rights, which monitors the war. It reported at least 41 fighters with the SDF, 34 Turkey-backed Syrian rebels and 17 civilians had been killed.
Turkey says two Turkish soldiers have been killed. Turkish authorities said two people were killed and three wounded by mortar shelling in the border town of Suruc, raising the death toll to nine civilians killed on the Turkish side.
A Kurdish official who oversees aid work in northeast Syria, Khaled Ibrahim, said water to Hasaka city and nearby areas was cut by Turkish shelling that damaged a pumping station. It had provided safe water for at least 400,000 people, UNICEF said.
Turkey says the purpose of its assault is to defeat the Kurdish YPG militia, which it sees as an enemy for its links to insurgents in Turkey. It says it aims to set up a "safe zone" inside Syria, where it can resettle many of the 3.6 million refugees it has been hosting.
Turkish President Tayyip Erdogan threatened to send refugees to Europe if the European Union did not back his assault. That prompted a furious response from the EU.
"We will never accept that refugees are weaponised and used to blackmail us," European Council President Donald Tusk tweeted. France said sanctions against Turkey would be discussed at an EU summit next week.
Responding to the wave of international criticism, Turkey's Foreign Minister Mevlut Cavusoglu defended its record of intervention in Syria in an opinion piece in the New York Times. Turkey had provided schools, hospitals and other services in other areas under its control, he wrote.
The Kurdish YPG is the main fighting element of the SDF, which has acted as the principal allies of the United States in a campaign that recaptured territory from Islamic State.
The SDF now holds most of the territory that once made up Islamic State's "caliphate" in Syria, and has been keeping thousands of fighters from the jihadist group in jail and tens of thousands of their family members in camps.
The SDF's Qamishlo said five Islamic State fighters had escaped from jail in Qamishli after nearby Turkish shelling.
In the al-Hol camp, home to thousands of women and children who emerged from the last Islamic State strongholds, Qamishlo said an uprising had taken place among foreigners.
"The Daesh (Islamic State) women rose against the internal security forces at al-Hol, they set ablaze tents and attacked the administrative and security offices there with stones and sticks," Qamishlo said.
Two Turkish officials said Ankara believed there were more than 1,000 Islamic State fighters, mostly foreigners, held in the part of Syria where Turkey aims to set up its safe zone. Turkey would aim to send them to their countries of origin.
RARE REPUBLICAN CRITICISM OF TRUMP
In the United States, Trump's decision to withhold protection from the Kurds has been one of the few issues to prompt criticism from his fellow Republicans, including leading allies on Capitol Hill such as Senator Lindsey Graham.
Trump said in a Twitter post on Thursday: "We have one of three choices: Send in thousands of troops and win Militarily, hit Turkey very hard Financially and with Sanctions, or mediate a deal between Turkey and the Kurds!."
"I hope we can mediate," Trump said when asked about the options by reporters. Without elaborating, he said the United States was "going to possibly do something very, very tough with respect to sanctions and other financial things" against Turkey.
Western countries' rejection of the Turkish offensive creates a rift within the NATO alliance, in which Turkey is the main Muslim member. NATO Secretary General Jens Stoltenberg said after talks with Cavusoglu in Istanbul that he expected Turkey to act with restraint. Cavusoglu said Ankara expected "strong solidarity" from the alliance.