“We have not abandoned the Kurds. Let me be clear about that,” Mr Esper told reporters.
“We have not abandoned them. Nobody green-lighted this operation by Turkey just the opposite. We pushed back very hard at all levels for the Turks not to commence this operation.”
Mr Esper spoke shortly before US forces came under Turkish artillery fire at a small outpost in northeastern Syria.
No Americans were hurt and the Turks insist the Americans were not targeted, but the strike shows how quickly the conflict is descending into turmoil.
Despite the criticism, Turkish President Recep Tayyip Erdogan has said his military will continue its controversial operation in northern Syria “no matter what anyone says”.
The United Nations estimates more than 70,000 people have fled their homes as forces push further into the region, with more than half a million people in border communities believed to be at risk.
Thousands have evacuated the villages of Ras Al-Ayn and Tal Abyad, according to the World Food Programme, with some leaving by foot and others loading their belongings into vehicles.
Mr Erdogan has been criticised by European leaders including EU Council President Donald Tusk since the offensive began three days ago, when US troops withdrew from the area.
Kurds fighting as the Syrian Democratic Forces (SDF) fought with US troops and played a vital role in defeating Islamic State, but now America has been accused of abandoning them.
The Turkish president issued a robust response to those against the action, saying: “We will never stop this step we have taken… We will not stop it no matter what anyone says.”
Mr Erdogan sees the Kurdish fighters based in northeast Syria as terrorists linked to an insurgency within Turkey, and has argued that the military action is necessary for its national security.
There are fears that the attack could enable Islamic State fighters held captive by the Kurds to escape and eventually rebuild the broken caliphate.
Those fears have been used a stick with which to beat President Trump, who received widespread criticism over the US withdrawal.
His critics, including Republicans and Democrats in Washington, said the decision was a betrayal of the Kurds.
Kurdish authorities have said camps sheltering displaced people are to be evacuated or moved after being shelled, with thousands to be relocated from Mabrouka camp near the Turkish border.
Another camp sheltering 13,000 people in Ain Issa could also be relocated.
While Turkey has carried out its assault with extreme force, it suffered its first military casualty since the campaign when one of its soldiers was pronounced dead on Friday morning.
That compares to 22 deaths within the SDF on Wednesday and Thursday.
In total, Turkey claims to have killed 49 “terrorists”, while six civilians in Turkey and seven in Syria have also died.
At least 277 people have died so far, with the offensive just three days old.
Mr Trump had warned he would impose crippling economic sanctions on Turkey if he was unhappy with the action, but has insisted he does not think the US should be relied on to police the region anymore.
He has tweeted that Washington has military, financial or diplomatic options to resolve the crisis if necessary.
One of his fellow Republicans, Liz Cheney, has said Mr Erdogan should “face serious consequences for mercilessly attacking our Kurdish allies in northern Syria”.
So far there has been no intervention from the US, and the UN Security Council has also failed to agree on what approach to take on the operation.
European countries have demanded a halt to the military action, while Russia – an ally to Syria – has called for “restraint” and “direct dialogue” between the two countries.