Amid growing chaos in Syria, Donald Trump has ordered all US troops to withdraw from the country’s north to avoid a bloody conflict between Turkey and formerly US-backed Kurdish fighters that “gets worse by the hour”, the defense secretary, Mark Esper, said on Sunday.

Reuters later reported that US officials speaking anonymously said the administration was considering plans to withdraw the bulk of American troops in the coming days, in what would be a faster-than-expected timeline.

The officials said the US was looking at several options but added it appeared likely the military would pull the majority of its forces in the coming days, instead of weeks. A full withdrawal could take two weeks or more, although even that could happen faster than expected, one official said.

Esper spoke to CBS’s Face the Nation and Fox News Sunday. Trump’s national security team planned to meet to assess the situation, he said, as the US continued to urge Turkish president Recep Tayyip Erdoğan to halt his incursion.

Asked if he thought Turkey, a Nato ally, would deliberately attack US troops in Syria, Esper said: “I don’t know whether they would or wouldn’t.”

He cited an incident on Friday in which a small number of troops fell under artillery fire at an observation post in the north. Esper called that an example of “indiscriminate fire” coming close to Americans, adding it was unclear whether that was an accident.

The Washington Post reported that US officials believe Turkish forces knew Americans were in the area.

Brett McGurk, the former US envoy to the global coalition against the Islamic State who resigned over Trump’s attempts to withdraw from Syria, told the paper: “Turkey wants us off the entire border region to a depth of 30km [20 miles]. Based on all the facts available, these were warning fires on a known location, not inadvertent rounds.”

Others may want to come in and fight for one side or the other. Let them! Donald Trump

Esper said he spoke to Trump on Saturday night amid growing signs the Turkish invasion, which began on Wednesday, was growing more dangerous.

“In the last 24 hours, we learned that they are likely to intend to expand their attack further south than originally planned – and to the west,” Esper said.

The American troops have been working for five years with a Kurd-led Syrian group known as the Syrian Democratic Forces to combat Islamic State. Turkey has long objected to the US-Kurd alliance because Turkey considers elements of that force to be terrorists tied to an insurgency inside Turkey.

The US had come to believe the Kurds are attempting to “cut a deal” with the Syrian army and Russia to counter the invading Turks, Esper said. As a result, Trump “directed that we begin a deliberate withdrawal of forces from northern Syria”.

On Sunday afternoon, Syrian state media said units from President Bashar al-Assad’s army were moving north to “confront Turkish aggression on Syrian territory”.

In tweets on Sunday, Trump said: “Very smart not to be involved in the intense fighting along the Turkish Border, for a change … Others may want to come in and fight for one side or the other. Let them!”

Esper said he would not discuss a timeline for the US pullback, but said it would be done “as safely and quickly as possible”. He did not say how many US troops would leave the north, but said they represented most of the troops in Syria.

The Pentagon had said before the Turkish operation began that the US military would not support it, and the US pulled about 30 special operations troops out of observation posts along the invasion route on the Syrian border.

It gets worse by the hour Mike Esper

Esper said he was aware of reports of hundreds of Isis prisoners escaping as a result of the Turkish invasion and of atrocities being committed against Syrian Kurds by members of a Turkish-supported Syrian Arab militia.

“It gets worse by the hour,” Esper said. “These are all the exact things” that US officials warned Erdoğan would probably happen if he ignored US urgings not to invade northern Syria.

More than 130,000 people have been displaced from rural areas around Tel Abyad and Ras al-Ayn as a result of the fighting, the United Nations said on Sunday.

Eliot Engel, the Democratic chair of the House foreign affairs committee, told NBC’s Meet the Press he could “think of nothing more disgusting in all the years I’ve been in Congress than what this president is allowing to happen with the Kurds.

“They have been our loyal and faithful allies for so many years, and after this, who again would trust the United States to be an ally of them?”

Esper said there was “no way” US forces could have stopped the Turks, who assembled a force of about 15,000 on the Syrian border, supported by air power.

“We did not sign up to fight Turkey, a longstanding Nato ally, on behalf of the [Kurdish-led Syrian Democratic Forces]. This is a terrible situation,” he said.

The Treasury secretary, Steven Mnuchin, held out the possibility of quick action to impose sanctions on Turkey, a move Trump has threatened if the Turks push too far.

“We’ll be taking in new information and we’re ready to go at a moment’s notice to put on sanctions,” Mnuchin told ABC’s This Week. “Now we have warned the Turks … They know what we will do if they don’t stop these activities.”

Trump tweeted that he was dealing with Lindsey Graham, the South Carolina Republican senator who has stringently criticised the withdrawal, “and many members of Congress, including Democrats, about imposing powerful sanctions on Turkey. Treasury is ready to go, additional legislation may be sought.

“There is great consensus on this. Turkey has asked that it not be done. Stay tuned!”