 -- When Turkey’s President Recep Tayyip Erdogan goes to Washington today for meetings with President Trump, it will be the first face-to-face meeting for the two leaders, who have traded warm words but now face growing differences between their countries.

With the U.S. and Turkey at odds over critical issues, it is unclear where Trump and Erdogan will be able to find common ground.

Still, the two will meet in the Oval Office and give a press statement afterward. Here are the top issues their delegations are expected to discuss.

Arming the Kurds and alienating a US ally

A big strain on the U.S.-Turkey relationship right now is over an announcement by the Trump administration last week that it will start to directly arm Kurdish rebels in Syria for the fight against ISIS.

The Kurdish group, known as the YPG, is part of the broader Syrian Democratic Forces, a multiethnic force that is backed by the U.S. and its coalition against ISIS and is seen as the most effective group in the fight, having made key gains in Syria’s northeast.

The Pentagon is now selling the YPG weapons like heavy machine guns, mortars and armored vehicles as it advances on ISIS’ self-declared capital of Raqqa, backed by American airpower.

The problem is that Turkey considers the YPG a terrorist organization because it maintains ties with the PKK, a Kurdish revolutionary group in Turkey. The U.S., the European Union and Turkey have sanctioned the PKK as a terrorist group. Ankara argues that any weapons given to the YPG are an existential threat to Turkey’s safety and sovereignty — an argument from which Erdogan's government will not back down.

“Every weapon seized by them is a threat to Turkey,” Turkish Foreign Minister Mevlut Cavusoglu said at a press conference alongside U.S. Defense Secretary James Mattis last week.

Tensions have gotten so high that one of Erdogan’s senior advisers, Ilnur Cevik, during a Turkish radio interview Wednesday, according to The Washington Times, warned that if YPG units and their American military advisers “go too far, our forces would not care if American armor is there,” referring to U.S. troops in Syria supporting the SDF. “All of a sudden, by accident, a few rockets can hit them.”

The Pentagon has tried to reassure Turkey that weapons supplied to the YPG will be “limited, mission-specific and metered out incrementally,” as well as closely monitored by the U.S.

The Trump administration has downplayed the differences between the U.S. and Turkey — NATO allies — as minor.

“It’s not always tidy, but we work out the issues,” said Mattis last week.

But so far, every reassurance by the U.S. has been met by resistance, and now Erdogan will take his case to the White House.

Salvaging an unraveling alliance

That fight over directly arming the Kurds reflects a larger fissure in the relationship between the U.S. and Turkey over their different strategic interests.

Turkey and the U.S. share an enemy in ISIS and remain committed to the fight against the terrorist group. But Turkey views Kurdish independence groups as its primary threat, and as every battlefield win against ISIS seems to lessen its immediate threat, there may be fewer shared interests holding the U.S. and Turkey together.

This is particularly evident in the increasingly anti-American rhetoric from Turkish leaders. Turks have “been fed a steady stream of anti-American incitement,” according to Michael Rubin of the conservative American Enterprise Institute.

“It’s probably only a matter of time before a Turkish soldier or officer decides to shoot at an American in the belief he is defending Turkey’s honor or fulfilling the unspoken desire of Erdogan,” Rubin warned.

The talk against the U.S. has caught the attention of the State Department, which warned American tourists in March that “an increase in anti-American rhetoric has the potential to inspire independent actors to carry out acts of violence against U.S. citizens.”

As Turkey turns away from its ally the U.S., it turns toward an old foe, Russia. The Turks signed an agreement just weeks ago with Russia and Iran — two top U.S. adversaries — to create “de-escalation zones” in Syria, establish a cease-fire in Syria and ultimately try to bring an end to the more than six-year-old civil war there. As Erdogan thaws relations with Putin, the Trump administration will have to work hard to convince Turkey’s president that the U.S. is a more loyal partner.

Handling human rights concerns

There may be one area where Erdogan can find a more willing partner in Trump than he did with the president’s predecessor.

President Obama walked a fine line with Turkey — supporting it while urging Erdogan’s government to respect human rights like freedom of the press and assembly. Trump has often thrown that approach out the door to salute the strongman on his increasingly dictatorial tactics.

When Erdogan won a referendum in April that will lead to abolishing the prime minister’s office and a weakening of the country’s parliament, Trump was one of the only world leaders to call Erdogan to congratulate him — even as critics and observers noted the election was rife with irregularities and that the changes threaten to choke off democracy in Turkey.

The move was part of a broader trend: an indifference to promoting human rights around the world and an embrace of authoritarian leaders in Egypt, the Philippines and elsewhere, regardless of their human rights records. Trump’s first trip abroad will be to Saudi Arabia this week, which has a stained history of human rights abuses.

An extradition dilemma or deal?

Given the high stakes of the meeting — and turmoil on the U.S. domestic front over reports that Trump shared classified information with Russia and his firing last week of FBI Director James Comey — Trump, the former businessman of “Art of the Deal” fame, could feel some pressure to reach a deal on something while Erdogan is in town, and Turkey may have just the thing.

Erdogan is demanding the extradition of Fethullah Gulen, a Turkish cleric living in self-imposed exile in Pennsylvania whom the Turkish president blames for a failed coup last summer and a host of other problems.

Michael Flynn, Trump’s former national security adviser, who has registered as a lobbyist on behalf of Turkey, advocated for Gulen’s extradition, and the Trump team was reportedly at one time considering “a covert step in the dead of night to whisk [Gulen] away,” James Woolsey, a former CIA director and Trump campaign adviser, told The Wall Street Journal.

The Justice Department under Obama asked Turkey to file the necessary paperwork to start the legal process for extradition, which drew Turkish protests. That process is said to be ongoing, but it is unclear what the administration’s current view on Gulen is.

In the meantime, the administration has started to raise the profile of Andrew Brunso, an American pastor held in Turkey. Secretary of State Rex Tillerson met with Brunson’s wife when he traveled to Turkey in March, and last week Trump met with Jay Sekulow, the chief counsel of the American Center for Law and Justice, who urged Trump to bring up Brunson’s case with Erdogan.

Last month Trump made an agreement with Egyptian President Abdel-Fattah el-Sissi to release American aid worker Aya Hijazi and her husband, who had been imprisoned on false charges. The victory is one Trump has touted often since then in interviews, and he could be looking for another win.

The administration has given no indication that it is studying any sort of swap with Turkey. Gulen is a permanent resident of the U.S., and the two countries’ extradition treaty allows refusal of extradition requests for offenses “of a political character” and for other reasons. But for two sides looking to paper over major differences, this could be an area for some movement.

ABC News’s Meghan Keneally contributed to this report.