Washington (CNN) Secretary of State Rex Tillerson's fledgling diplomatic skills are being put to the test as he visits Turkey to discuss the fight against ISIS and then Belgium for a meeting of NATO foreign ministers this week.

Tillerson's stop in Turkey Thursday likely poses the real challenge. Trump's top diplomat is there, on the eve of a massive push against ISIS' Syrian stronghold Raqqa, to persuade Ankara that its sworn enemy -- the Kurds -- are critical partners in the effort to defeat the terror organization.

In Brussels, Tillerson will reprise the Trump administration's refrain that it's "essential" NATO partners boost their defense spending and do more to fight terrorism. He's also likely to reaffirm the US commitment to Europe and NATO, something some allies privately have their doubts about.

Kurds aren't the only source of friction in the US-Turkey relationship. The US has yet to hand over the Turkish cleric Fethullah Gulen, a US resident whom President Recep Tayyip Erdogan accuses of orchestrating a coup attempt last summer. This week, US officials arrested the deputy CEO of a Turkish bank closely allied to the country's elites for violating sanctions against Iran.

And a day before Tillerson left for Ankara, the State Department warned Americans of increased terror threats in Turkey, asking them to "carefully consider" whether they should travel there.

"It all makes for a difficult diplomatic problem for Tillerson to figure out how to manage," said John Hannah, a senior counselor at the Washington-based Foundation for Defense of Democracies. "How do we destroy ISIS, while maintaining a relationship with a critical NATO ally?"

A senior State Department official told CNN that Tillerson delivered the message to Erdogan 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."

Tillerson's visit also comes ahead of a Turkish referendum that would dramatically expand Erdogan's executive power and allow him to remain as president for another 12 years.

JUST WATCHED Turkey considers expanding presidential powers Replay More Videos ... MUST WATCH Turkey considers expanding presidential powers 02:17

James Jeffrey, a former US ambassador to Turkey now at The Washington Institute for Near East Policy, predicted Erdogan is unlikely to agree to any of Tillerson's demands before the referendum, because he needs critical votes from nationalist parties that are vehemently anti-Kurd.

"This limits Erdogan's ability to try to cut deals of any sort on the Kurds," Jeffrey said. "He doesn't want to see the Kurds expand their territory. He doesn't want the US to be a permanent supporter of the Kurds and thinks the Americans are naive to work with them."

The State Department official said that while Tillerson "can't promise anything solid" to Turkey about the Kurds, he was going to "imply this is a circumstantial relationship and any aspirations the Kurds have beyond this current situation will not be met with our cooperation."

As Jeffrey put it, "Tillerson's mission is not just to calm him about the inevitable push on Raqqa with the support of the Kurds, but explain the larger plan to contain (Syrian President Bashar Al-)Assad, Iran and Russia in the region, which is something President Obama was never able to do."

JUST WATCHED Can ISIS ever be eradicated? Replay More Videos ... MUST WATCH Can ISIS ever be eradicated? 01:34

Notably, Tillerson did not meet with any members of the Turkish opposition while in Ankara, a move Jeffrey called a mistake.

"It incorrectly, but understandably, signals the United States is rooting for Erdogan. And even if we were, it is totally wrong to interfere," he said. "But given how fragile and critical relations are with Erdogan, perhaps there is some just justification."

Hannah, a former Middle East adviser to Vice President Dick Cheney, noted that Tillerson "does have experience dealing with some very tough leaders" in his former role as ExxonMobil CEO. But he added that shepherding the US through this tricky time with Turkey will require "a genuinely unified US government policy to get us through in one piece."

Meanwhile, Turkey announced Wednesday that it is ending its operation against ISIS in northern Syria. "Operation Euphrates Shield" began last August when Turkey sent ground troops, tanks and warplanes to support Free Syrian Army rebels push ISIS away from the Turkish border.

All this takes place against a backdrop of questions about Trump administration ties to Turkey.

The President's former national security adviser, retired Lt. Gen. Michael Flynn, disclosed in early March that he'd worked as a foreign agent representing Turkish government interests during the presidential campaign.

Former CIA Director James Woolsey claimed in an interview on CNN Friday that at a meeting he himself attended during the campaign, Flynn met with Turkish government ministers to discuss how to return Gulen to Turkey without going through the legal extradition process.

JUST WATCHED Former CIA director: Flynn meeting suspicious Replay More Videos ... MUST WATCH Former CIA director: Flynn meeting suspicious 02:20

A spokesman for Flynn flatly denied Woolsey's characterization of the meeting.

"The claim made by Mr. Woolsey that General Flynn, or anyone else in attendance, discussed physical removal of Mr. Gulen from the United States during a meeting with Turkish officials in New York is false," Flynn spokesman Price Floyd said in a statement. "No such discussion occurred. Nor did Mr. Woolsey ever inform General Flynn that he had any concerns whatsoever regarding the meeting, either before he chose to attend, or afterwards."

The Trump Organization is also active in Turkey. Two skyscrapers in Istanbul bear Trump's name, yielding his family millions of dollars in licensing fees. After Trump first floated the idea of a Muslim ban during the campaign, Erdogan suggested his name be removed from the buildings. Those suggestions stopped after candidate Trump later said Erdogan shouldn't be criticized for his crackdown after the failed coup.

A senior State Department official characterized Tillerson's meeting with Erdogan and his foreign minister as "a continuation of a series of high-level engagements with Turkey" by Trump and other members of his government.

JUST WATCHED Assad: US troops in Syria are 'invaders' Replay More Videos ... MUST WATCH Assad: US troops in Syria are 'invaders' 01:24

Tillerson also discussed Iran, Syria, Iraq, trade and investment, and offered condolences on the Turkish loss of life to terrorism and appreciation for their work to defeat ISIS -- raising the prospect of an uncomfortable exchange over the participation of the Kurds in Syria in this fight.

Trump campaigned on a promise to speed up the fight against ISIS and defeat the group, which would require the help of the fierce fighting force of Kurds called the YPG -- which Erdogan sees as an extension of Turkish Kurds that are at war with Turkey right now.

The US acknowledges connections between the two groups, but sees them as two separate forces. Turkish officials, however, argue that weapons and support the US gives the YPG in Syria end up in the hands of the PKK in Turkey that will use them to kill Turks.

"They see it as an existential threat and don't really draw any distinctions," Hannah said.

A second senior State Department official, discussing Tillerson's trip to Ankara, said that the US is "of course very mindful of Turkey's concerns and this is something, of course, that will continue to be a topic of conversation."

The US could delay the assault on Raqqa and eventually replace the YPG with other forces it trains, but "you're going to lose a lot of time, which will create political problems in the US as well as the strategic problems," Hannah said.

Security officials believe the city serves as the heart of ISIS planning for external operations -- the kinds of terror attacks seen in Paris, Brussels and Nice in 2015 and 2016.

"The longer you allow Raqqa to exist as the operational heart of the Caliphate, the more likely they're going to be able to launch the kinds of attacks we saw last year," Hannah said. "It's a genuine and very serious, political, military and diplomatic dilemma that the US is going to have to manage, assuming that the YPG is going to be the tip of the spear in Raqqa."

The ISIS fight, along with efforts to help Ukraine deal with Russian aggression, will be topics in Brussels, where Trump's global envoy will meet with his NATO counterparts. That meeting was hurriedly rescheduled after Tillerson initially said he'd be skipping it but making time to go to Russia later in the month. The NATO gathering will pave the way for a leaders' meeting in two months.