Tension has mounted in the past year between the Kurdish YPG force and its allies on one hand and Turkish-backed rebel groups fighting President Bashar al-Assad on the other, in the Aleppo region.
Turkish forces last week launched a two-pronged operation against IS and Kurdish fighters from the People's Protection Units (YPG) inside Syria.
He told reporters at the Pentagon that Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, spoke to his Turkish counterpart Sunday. They have been clashing with US -backed Kurdish Syrian forces around the town to try to halt their advance.
Days earlier the Kurdistan Worker's Party, the PKK, claimed responsibility for a deadly explosion at a police station - also in southeastern Turkey - that killed 11 police officers and wounded scores more. However, it is unclear if the two reports are on the same incident.
Turket sending troops and tanks across the border into Syria last week, supported by the United States, should add at least one element of clarity to USA policy and to the lineup in the ongoing multifaceted Middle Eastern war.
"The YPG is engaged in ethnic cleansing, they are placing who they want to in those places", Turkish Foreign Minister Mevlut Cavusoglu said in Ankara, demanding Kurdish forces withdraw east of the Euphrates river, a natural boundary with areas of eastern Syria under Kurdish control.
Al Jazeera's Hashem Ahelbarra, reporting from Gaziantep on Turkey's border with Syria, said: "The Turkish army has intensified its military operation following the death of a Turkish soldier".
But he also said it was "not possible" to defeat Daesh through only airstrikes alone. Our operations against the separatist organization [YPG] will continue without interruption.
"We've called on both sides to not fight with one another, to continue to focus the fight on ISIL", Defense Secretary Ashton Carter said, using an acronym for the Islamic State group (IS).
Erdogan's message was meant to mark Turkey's Victory Day celebrations on Tuesday.
The Turkish military had carried out 61 artillery strikes on 20 targets around Jarablus in 24 hours, Turkey's state news agency Anadolu reported on Monday. The move was also aimed at halting advances by the Syrian Kurdish forces.
The Turkish campaign pre-empted action by Kurdish-backed forces which had sought to get to Jarablus first. The Damascus government condemned the intervention as a breach of its sovereignty.
The United States has served as protector and supporter of the Kurds, first in Iraq and now in Syria, since the end of the first Gulf War against Iraq in 1991, when Iraqi President Saddam Hussein began putting them back where he believed they belonged, in a subordinate position.
A spokesman for the autonomous Kurdish region in Syria said on Monday, August 29 that local military forces in the Syrian cities of Manbij and Jarablus are being reinforced, but not by Kurdish YPG militia, Reuters says.
Add to all that the recent coup attempt in Turkey - which Ankara believes the U.S. was far too slow to condemn - and there's a significant risk of increased instability in a region already torn apart by five years of civil war.
Ankara has frequently voiced its concern over YPG activity along its borders and has been adamant in its stance against a de facto Kurdish state in northern Syria.
As the death toll rises, with reports of civilian casualties, Turkey's North Atlantic Treaty Organisation ally the U.S., which backs the YPG, called on all armed actors in the fighting to stand down and focus on battling the so-called Islamic State group. It did not say which group was targeted.