The People's Protection Units (YPG) and the Peshmerga in Iraq -- both Kurdish groups -- said at least 25 of their fighters had been killed in the strikes on Tuesday. Ankara denies deliberately targeting them.
The YPG fights in the Syrian Democratic Forces (SDF), a rebel alliance armed and supported by the United States, but is considered a terrorist group by the Turkish government.
The airstrikes -- targeting the Sinjar Mountains northern Iraq and the Karachok Mountains in northeastern Syria-- and the reported cross-border skirmishes since then, have added yet another complication to an already complex situation.
Now US troops are trying to stop the outbreak of violence between two of their closest allies in the region from escalating.
"The patrols' purpose is to discourage escalation and violence between two of our most trusted (counter-ISIS) partners and reinforce the US commitment to both Turkey and the SDF in their fight against ISIS," a statement from the US-led joint command said.
"We ask both of our partners to focus their efforts on ISIS. ISIS poses the greatest threat to peace and stability in the region, and indeed the entire world."
Turkey has made clear it will use force to prevent the development of a Kurdish-controlled area on its Syrian doorstep.
The patrols began on Friday and are being conducted mainly by special operations forces, a US official told CNN. They are using armored vehicles and are flying US flags for transparency.
Turkish President Recep Tayyip Erdogan was asked by Turkish state-run news agency Anadolu about the border patrol, and said Turkey is "seriously concerned to see US flags in a convoy that has YPG rags on it."
He said he would bring up the issue with President Donald Trump during his planned visit to Washington on May 16 -- and called for the coordination between the US and YPG to "come to an end."
"We are two NATO member countries, and strategic allies will be seriously bothered by it. As we always say we will take care of our own business."
Turkish officials said the airstrikes were targeting members of the Kurdistan Workers Party (PKK), considered a terrorist group by both Turkey and the United States. Seventy people were killed, they said. Turkey often describes the YPG as a Syrian branch of the PKK.
Ankara offered condolences to the Kurdish Regional Government President Masoud Barzani for the deaths of the Peshmerga forces, but there were no apologies for the deaths of the US-allied YPG.
Turkish officials said they gave the US and Russia warning that the strikes were coming, but a senior US defense official said they were only given an hour, nowhere near enough time to evacuate the rebels.
SDF gains against ISIS
Meanwhile, on Sunday, the Syrian Democratic Forces (SDF), announced significant advances in the fight against ISIS near Raqqa, ISIS' self-declared capital. In a statement, the SDF said it had captured six more neighborhoods in addition to the radio station building from ISIS in the city of Tabqa, west of Raqqa.
For weeks rebel fighters, backed up by US forces
, have fought to try and take control of the city and its dam. The Tabqa Dam is located 25 miles west of Raqqa, and supplies electric power to a wide area of Syria, according to the US. The area has been under ISIS control since 2013.
Retaking the dam is considered a vital step toward further isolating the area around Raqqa and eventually recapturing the city.
Erdogan bans Wikipedia, fires civil servants
Tuesday's airstrikes came just over a week after Erdogan won a historic referendum that granted him sweeping new powers and could cement his position as Turkey's leader until 2029. It is just one of the Turkish government's bold moves since the election win.
On Saturday, the government issued a decree banning television matchmaking shows and blocked access to Wikipedia over content that Turkey said linked the nation to terror activity.
Turkey warned Wikipedia to remove the content, but the nonprofit encyclopedia refused, the Turkish Ministry of Transport, Maritime Affairs and Communications said. Once Wikipedia meets Turkey's demands, the access ban will be lifted, it said.
Wikimedia Foundation, a nonprofit organization that supports Wikipedia, said it was actively working to seek a judicial review of the decision.
Turkey -- a member of NATO and a US ally -- appears to be taking a decided authoritarian turn when it comes to freedom of information.
It has blocked social media in the past, such as Twitter
, and the Committee to Protect Journalists
regards the country as "the world's worst jailer of journalists."
Thousands more "opposition figures" have been arrested in the past week, in the latest stage of a state purge following a failed military coup last July that has seen tens of thousands of people detained.
On Saturday alone, nearly 4,000 civil employees were fired, according to a decree announced on a government website. The decree said soldiers and academic personnel were among the 3,974 state employees dismissed.
Eighteen academic foundations, 14 nongovernmental organizations and 13 health groups were also shuttered due to activities against national security, Anadollu reported.
Turkish voters this month passed an 18-article constitutional reform package
to transform the country's parliamentary system into a powerful executive presidency.
The plan, put forward by the ruling Justice and Development Party, gives Erdogan sweeping and largely unchecked powers.
International election monitors delivered a scathing verdict on the conduct of the referendum, but Erdogan denied his new powers were a move toward dictatorship