(CNN) The Trump administration doubled down Thursday on prioritizing the fight against ISIS over ending the Syrian civil war and getting rid of its main protagonist, President Bashar al-Assad -- a suggestion that was swiftly criticized by hawks on the Hill.

Indicating a possible shift in US policy on the war in Syria from the days of the Obama administration, Secretary of State Rex Tillerson said on a trip to Turkey that the "longer-term status of President Assad will be decided by the Syrian people."

And in New York, US Ambassador to the UN Nikki Haley was even stronger about the Trump administration's decision not to push for Assad's departure. "Our priority is no longer to sit and focus on getting Assad out," Haley told wire reporters Thursday, according to AFP.

"Do we think he's a hindrance? Yes," she said. "Are we going to sit there and focus on getting him out? No."

However, a US official told CNN that Haley's remarks were misunderstood. The official said the US ambassador was not giving Assad a free pass, and she called Assad a "war criminal" in an appearance Wednesday at the Council on Foreign Relations in New York City.

The official explained to CNN that the priorities of the administration now are not exclusively about Assad, but also defeating ISIS, stopping the spread of Iran's influence, protecting US allies in the region and trying to end the Syrian civil war.

If the US does definitively abandon the policy of requiring Assad's departure -- a position articulated by the Obama administration -- it would put its policy closer in line with Russia, which supports Assad, and at odds with allies in Europe and in Turkey, where Tillerson downplayed frictions that are already straining that alliance.

The comments drew heavy criticism from Sens. John McCain and Lindsey Graham, Republicans who have long advocated for an increased US military presence in Syria against Assad and his Russian allies.

"This overlooks the tragic reality that the Syrian people cannot decide the fate of Assad or the future of their country when they are being slaughtered by Assad's barrel bombs," Arizona's McCain said in a statement.

Meanwhile, South Carolina's Graham said, "If the press reports are accurate and the Trump Administration is no longer focusing on removing Assad, I fear it will be the biggest mistake since President Obama failed to act after drawing a red line against Assad's use of chemical weapons."

In Turkey, Tillerson's fledgling diplomatic skills were put to the test in his most challenging diplomatic mission since taking office. He met for two hours behind closed doors with President Recep Tayyip Erdogan on the eve of a massive push against ISIS' Syrian stronghold of Raqqa. Tillerson's goal was to persuade Erdogan that the Kurds -- the Turks' sworn enemy -- are critical partners in the effort to defeat the terror organization.

The top US diplomat dodged questions at the news conference about US support for the Kurdish militia YPG, which the US considers the strongest fighters to go after ISIS, but said the two countries discussed "alternatives." His Turkish counterpart signaled that US support for the YPG remains one of a few stumbling blocks in US-Turkey relations.

"What we discussed today are options that are available to us," Tillerson said after a meeting with Foreign Minister Mevlut Cavusoglu. "They are difficult options. Let me be very frank. It isn't easy. They are difficult choices that have to be made."

Cavusoglu decried the US insistence on seeing Turkish Kurds at war with Turkey as separate from the YPG militia in Syria, which has received arms and support from Washington. He told reporters, "It is a sorrow for us that this sort of support has been extended (by the US to the YPG)."

A senior State Department official told CNN before the talks that Tillerson's message to Erdogan would be that the US is committed to working with the Kurds in the offensive against Raqqa.

Tillerson was set to tell the Turks that "we are going to do what we have to do," the official said. "It's not a happy message and they aren't going to like it, but this is what he has to tell them." The official continued that Tillerson also told them that "our priority is the long-term relationship with the Turks -- but at the moment, the emerging crisis requires us to use the folks who will fight."

Cavusoglu said that US support for the Kurdish forces belonging to the YPG militia, which it considers terrorists, has saddened Turkey and harmed efforts to reset the US-Turkey relationship after the election of President Donald Trump.

"We can fight Daesh together," Mr. Cavusoglu said, using the Arabic word for ISIS. But he added that "it is not correct to fight against one terrorist organization while co-operating with another."

He said there was no difference between the YPG militias working with the United States in Syria and the PKK, a group that has launched terror attacks against Turkey and which the US has branded a terrorist organization. While Tillerson noted Turkey had suffered attacks at the hands of PKK, he did not equate the group with the YPG.

Kurds aren't the only source of friction in the US relationship with Turkey, a NATO ally that hosts two US military bases.

Key among them is that the US has yet to hand over the Turkish cleric Fethullah Gulen, a US resident whom Erdogan accuses of orchestrating a coup attempt last summer.

Turkey's demand that Washington extradite Gulen, whom Turkey blames for leading last year's failed coup, loomed over Tillerson's talks. Gulen denies involvement in the attempt.

Cavusoglu said Turkey provided ample evidence to the US and said that Attorney General Jeff Sessions had pledged to "evaluate the documents meticulously." He said Turkey wants to see "concrete steps," and asked for the US to issue a provisional arrest warrant for Gulen while the extradition process moves forward

"We need to take mutual steps to put relations with the United States back on track," he said.