Turkey says its ground forces have crossed the border into northern Syria, after it began a military operation against Kurdish fighters on Wednesday
A spokesperson for the Syrian Democratic Forces (SDF) said the airstrikes have caused "a huge panic among people of the region."
There are reports a Kurdish fighter has been killed and six others wounded, a Syrian war monitor said.
Turkish President Recep Tayyip Erdogan announced his country had begun an incursion into Syria.
Turkish reports claim suspected Syrian Kurdish forces across the border in Tal Abyad are being shelled by artillery units.
President Donald Trump says the U.S. does not endorse Turkey's assault on northern Syria and has made it clear to Ankara that it's incursion against Kurdish fighters who helped the U.S. battle the Islamic State is a "bad idea."
In a statement Wednesday, Trump said no American soldiers are in the area being invaded. Earlier, Trump ordered U.S. forces out of the area, prompting criticism that he was abandoning an American ally.
Trump says he does not want the U.S. to fight "these endless, senseless wars."
He says he will hold Turkey to its commitment to protect civilians and religious minorities, including Christians, and ensure the invasion does not create a humanitarian crisis. He also says Turkey must make sure that IS fighters held captive in Syria remain detained.
Egypt has condemned "in the strongest words" Turkey's military operation into northern Syria and has called it an "aggression" against Syria's sovereignty.
Egypt's Foreign Ministry in a statement on Wednesday called for the U.N. Security Council to halt "any attempts to occupy Syrian territories or change the demographics in northern Syria."
Meanwhile Turkey's state-run news agency, Anadolu Agency, reports two mortar shells were fired from Ras al Ayn in Kurdish Syria into the town of Ceylanpinar.
No casualties are reported in the Turkish town.
On Twitter, President Erdogan said: "Our goal is to eliminate the terrorist corridor to be formed on our southern border to bring peace and security to the region."
Turkey has been massing troops for days in preparation for an attack against Kurdish fighters in northeast Syria that Ankara considers a terrorist organisation.
For months Turkey has threatened to launch a military operation to drive away Syrian Kurdish fighters from a border region east of the Euphrates River.
ITV News Correspondent Emma Murphy, who is at the Turkey-Syria border, tweeted reports were coming in of a strike in Ain Issa, near the SDF headquarters.
Anadolu Agency reports howitzers pounded Tal Abyad after Erdogan announced the start of the operation, with the offensive beginning at 1pm BST.
Syrians in the north-eastern border town of Ras al-Ayn are protesting against Turkey's military offensive
Earlier, Turkish television reports said Turkish jets were carrying out airstrikes on Syrian Kurdish positions in Tal Abyad and showed smoke billowing from the targeted areas.
Turkey's Foreign Ministry said ambassadors of the United Nations Security Council's five permanent members, including US ambassador David Satterfield, were being briefed on the operation.
Mr Erdogan said the operation - named Peace Spring - aims to eradicate "the threat of terror" against Turkey.
Earlier, Turkish television reports said Turkish jets had bombed Syrian Kurdish positions across the border from Turkey.
Turkey had long threatened an attack on the Kurdish fighters whom Ankara considers terrorists.
How has the world reacted to the operation?
The secretary-general of NATO is urging Turkey not to "further destabilize the region" through its military action in northern Syria.
Jens Stoltenberg told a news conference in Rome that Turkey, a NATO ally, "has legitimate security concerns," having suffered "horrendous terrorist attacks" and hosting thousands of refugees.
He said NATO has been informed about Turkey's ongoing operation in northern Syria. And he added "it is important to avoid actions that may further destabilize the region, escalate tensions and cause more human suffering."
Mr Stoltenberg will discuss the military action with Turkey's leader on Friday in Istanbul.
Speaking to EU lawmakers on Wednesday, European Commission President Jean-Claude Juncker said: "I call on Turkey as well as on the other actors to act with restraint and to stop operations already, as we are speaking, underway."
While acknowledging that Turkey has security concerns on its border with Syria, Mr Juncker says that "if the Turkish plan involves the creation of a so-called safe zone, don't expect the European Union to pay for any of it."
Germany's foreign minister is condemning Turkey's offensive and called on Ankara to end the military action, saying it threatened "a further humanitarian catastrophe and further displacement of persons."
Foreign Minister Heiko Maas said in a statement Wednesday that "we condemn the Turkish offensive in the northeast of Syria in the strongest possible terms."
What has US President Donald Trump said?
The move into Syria comes just days after Donald Trump declared US troops would withdraw from the "endless war" in the Middle East.
Acknowledging that "the Kurds fought with us" against so-called Islamic State, Mr Trump claimed they "were paid massive amounts of money and equipment to do so".
Syrian Kurdish fighters, known as the Syrian Democratic Forces (SDF), called the US's move a "stab in the back" which risked gains made in the fight against the so-called Islamic State group.
They continued they would "not hesitate for a moment in defending our people" against Turkish troops, adding that it has lost 11,000 fighters in the war against IS in Syria.
A Turkish attack would lead to a resurgence of so-called Islamic State it said.
Sleeper cells of the terror group are already plotting to break free some 12,000 militants detained by Syrian Kurdish fighters in north-eastern Syria in a "threat to local and international security".
The US President was widely criticised, even from Republican allies, for what has been seen as his abandonment of the Kurds, who have fought alongside Americans for years.
In a series of tweets posted on Monday, he threatened to destroy the Turkish economy if it acted in a way he considered - in what he said was his "great and unmatched wisdom" - "off-limits".
“If Turkey does anything that I, in my great and unmatched wisdom, consider to be off limits, I will totally destroy and obliterate the economy of Turkey (I’ve done before!),” he said on Twitter.