Overnight, Turkey hit dozens of targets in northern Syria as well as northern Iraq, a week after a bomb attack in Istanbul killed six people and left 81 wounded, which Ankara blamed on the Kurdistan Workers' Party (PKK).
Kurdish groups and authorities have denied responsibility for the November 13 bombing, which revived bitter memories of a wave of attacks in Turkey between 2015 and 2017.
Rocket fire from Syrian territory on Monday killed at least two people, including a child, in Turkey's border town of Karkamis, top officials said.
"Competent authorities, our defence ministry and chief of staff will together decide the level of force that should be used by our ground forces," Erdogan said.
Turkey's raids, mainly targeting positions held by Kurdish forces in northern and northeastern Syria, killed at least 37 people and wounded 70 others, according to the Syrian Observatory for Human Rights (SOHR), a Britain-based monitoring group.
Ankara said the targeted Kurdish bases were being used to launch "terrorist" attacks on Turkish soil.
On Monday, thousands gathered to bury 11 people who died in Al-Malikiyah in Syria's far northeast, including a journalist working for a Kurdish news agency, with the caskets draped in red-white-and-green Kurdish flags.
"We urge the world, all those who care about human rights and the great powers" to press Turkey to stop its strikes that "target us with planes and drones", a mourner named Shaaban, 58, told AFP during the funerals.
Washington expressed its condolences over the loss of civilian life in Syria and Turkey and urged a de-escalation in Syria.
"We urge de-escalation in Syria to protect civilian life and support the common goal of defeating ISIS," State Department spokesperson Ned Price said in a statement, referring to the fight against the jihadist Islamic State group.
"We continue to oppose any uncoordinated military action in Iraq that violates Iraq's sovereignty," he added.
In Berlin, the German foreign ministry also urged Turkey to "react proportionally and to respect international law", adding that "civilians at all times must be protected".
Turkey's latest military push could create problems for its complex relations with its Western allies -- particularly the United States, which has relied mostly on Syrian Kurdish militia forces in its fight against IS jihadists.
SOHR said Kurdish fighters and Syrian soldiers bore the brunt of the casualties during the attacks in the areas of Raqa and Hassake in the northeast and Aleppo in the north.
The Kurdish-led Syrian Democratic Forces (SDF), among those attacked, said Turkey launched new air strikes on Monday.
The strikes also targeted PKK bases in mountainous northern Iraq and bases of the Kurdish People's Protection Units (YPG) in Syria, the Turkish defence ministry said.
The PKK has waged a bloody insurgency for decades and is designated a terror group by Ankara and its Western allies.
An exchange of artillery fire between Turkish forces backed by Syrian auxiliaries and the SDF also broke out after Karkamis was hit, according to an AFP correspondent.
'70 planes and drones'
Ankara considers the YPG to be a PKK-affiliated terror group.
Erdogan said "70 planes and drones" that "penetrated 140 kilometres (87 miles) into northern Iraq and 20 kilometres into northern Syria" carried out the weekend strikes.
Erdogan said he had had "no discussion" with either US President Joe Biden or Russian President Vladimir Putin "on the subject of the operation".
Turkey has often accused Washington of supplying Kurdish forces with weapons while Russia backs pro-Damascus militias in the region.
Between 2016 and 2019, Turkey launched three large-scale operations in northern Syria against Kurdish groups.
Dozens of protesters opposed to the Turkish raids in Syria and Iraq were arrested in Ankara and Istanbul late Monday, after they had gathered at the call of the pro-Kurdish HDP party, AFP journalists said.