"The nine civilians were executed at different moments south of the town of Tal Abyad", the Syrian Observatory for Human Rights said.
But the SDF said Turkish troops had only entered one neighbourhood in Ras al-Ain's industrial district after hours of heavy shelling had pressed its own forces into a "tactical retreat" from that area.
Trump has faced strong bipartisan criticism for withdrawing some U.S. troops from the region ahead of the Turkish assault, a move many see as leaving Kurdish militia in the lurch after they aided Washington in fighting the extremist group "Islamic State" (IS).
There has been fierce worldwide criticism of the assault and concern about its humanitarian consequences.
The United States has again warned Turkey of what it calls "consequences" if its military offensive into northeast Syria carries on.
Germany and France, other fellow North Atlantic Treaty Organisation allies, said on Saturday they were banning some arms exports to Turkey, while the head of the 22-member Arab League called for the United Nations Security Council to take measures to force Turkey to halt its "invasion".
Senator Lambie, who served as a corporal in the Australian army in the early 1990s, said Turkey's military offensive in the Kurdish-majority area was scary.
The move immediately raised concerns that the United States was abandoning Syrian Kurds, who have been the closest USA partner in counter-terrorism operations against the Islamic State.
Russian President Vladimir Putin said Syria must be freed from foreign military presence. "This applies to all states", Mr Putin told RT, Arabik Sky News and Al Arabiya in an interview.
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Aid agencies have warned of a humanitarian crisis, with almost a half-million people at risk in northeastern Syria. On Friday , the SDF said several ISIS prisoners had escaped a facility in Qamishli after Turkey forces bombed it.
Al Jazeera's Charles Stratford, reporting from Akcakale on the Turkey-Syria border, said there had been reports of "clashes in surrounding villages" following the competing claims over control of Ras al-Ain.
With little leverage left in the game, Syria's Kurds - viewed by Ankara as "terrorists" - may have to thaw ties with President Bashar al-Assad's Russian-backed regime.
"It's less secure, less stable and they fight", he said.
The YPG has been the backbone of the Kurdish-led Syrian Democratic Forces (SDP) who were the main partner on the ground in the US-led campaign against the militant Islamic State (IS) group.
Dozens of Israelis joined thousands of others across Europe Saturday protesting against the Turkish assault on Kurds in northern Syria.
Khalaf was the secretary general of a newly established party, the Future Party of Syria.
Speakers in Jerusalem called on the government to take more forceful action, including sending back Turkey's ambassador, cutting off arms sales to Ankara and using the Israeli air force to create a no-fly zone.
"Turkey wants us off the the entire border region to a depth of 30 kilometres", he said.
The Kurdish militia known as the People's Protect Units, or YPG, has formed the backbone of USA efforts in northeastern Syria and collaborated with USA troops, but Turkey considers the group to be part of a Kurdish movement, the PKK, that it deems a terrorist organisation.