(CNN) Turkey's President Recep Tayyip Erdogan will likely take a wishlist to his meeting with US President Donald Trump on Tuesday, and at the very top will be calls to scrap a US plan to arm Kurdish rebels in Syria.

Turkey and the United States are key NATO allies, but their relationship has been complicated by the US's strategy on Syria, and by Washington's refusal to extradite a Turkish cleric who Erdogan claims was behind the failed coup in Turkey last year.

Here what's likely to be high on the agenda at their talks:

1. US arming Kurdish fighters

Turkey lashed out last week after the Pentagon announced plans to arm members of the Kurdish People's Protection Unit (YPG) fighting ISIS in Syria. Erdogan called for the plan to be "reversed immediately" and promised his supporters he'd discuss the issue with Trump at the White House meeting on Tuesday.

The YPG fights in a coalition of rebel groups that the US considers its main ally in the Syrian conflict, but Turkish officials see the unit as a terrorist organization linked to an insurgency movement in the south of Turkey.

"We want to believe that our allies would prefer to be side-by-side with ourselves rather than with the terror groups," Erdogan told reporters last week, shortly after the Pentagon announcement, according to AFP.

US forces with the Kurdish People's Protection Units (YPG) fighters patroling part of the Turkish-Syrian border on April 28.

"It is not an ideal political approach to fight against a terrorist organization with the help of another terrorist organization."

The Pentagon argues that the YPG, and its allied groups, are the most capable forces on the ground and will be crucial as the anti-ISIS fight in Syria enters a critical phase: the battle for the group's de facto capital, Raqqa.

The Obama administration mulled arming the Kurds for many years, but kept the idea on the backburner to avoid confrontation with Turkey.

But the government of then-US President Barack Obama did arm the Kurds' Arab allies, a move widely seen as a way for the administration to indirectly, or quietly, arm the YPG without upsetting Turkey.

Ankara has long expressed its outrage over the US' support for the YPG, but had largely tolerated it.

2. Turkey's relationship with Russia over Syria

Turkey, along with Russia and Iran, is brokering ceasefire talks aimed at ending Syria's six-year war.

The ceasefire talks -- held in Astana, Kazakhstan -- were spearheaded by Russia and were widely seen as a way to sideline the United States from the process. While that move rattled the Obama administration, the Astana talks now seem to have been accepted by Trump and other Western leaders.

The United Nations has for years failed to make crucial decisions in resolving the Syrian conflict as Russia repeatedly used its veto power to shoot down resolutions.

Russia is the most powerful ally of Syrian President Bashar al-Assad's regime , and while much of the West supports Assad's removal, Russia has insisted that he stay in charge.

Turkey has become a close ally of Russia in the past year, marking an extraordinary U-turn in a once rocky relationship, and Turkey is showing signs that it is less interested in having allies in the West.

Trump appeared to be backing away from the Syrian conflict at the start of his term, but that changed last month when he ordered the country's first strikes on Syrian regime targets, following a horrific chemical attack blamed on the Assad regime

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3. Extradition of Erdogan's rival Gulen

Erdogan and Turkish officials have long pressed the United States to extradite Fetullah Gulen , a friend-turned-foe of Erdogan's, who has been in self-imposed exile in Pennsylvania since 1999.

Erdogan believes Gulen was behind a failed military coup in July last year, but the US has said there is not enough evidence to send the 76-year-old Muslim cleric back to Turkey.

Gulen has repeatedly denied involvement in the coup attempt.

Erdogan told reporters last week that he would "present some documents and information" on Gulen at the Trump meeting.

Gulen is the leader of a popular movement called Hizmet, but the Turkish government refers to his group as the Fethullah Gulen Terrorist Organization (FETO).

Erdogan has in the past said that at some point the US will have to choose between Turkey and Gulen.

"In my opinion, the US shouldn't be an incubation place for FETO," he told reporters last week.

In an exclusive interview with CNN last month, Erdogan said that he planned to have a "tete-a-tete" with Trump on Gulen, claiming that there was now sufficient evidence pointing to the cleric as the attempted coup's mastermind.

"We are going to sit down with him. We're going to talk about these aspects in a very detailed fashion. We have not been made a promise yet. I am hopeful -- I'm hopeful and I'm going to preserve that hope," he said.

Erdogan and his government called a state of emergency following the failed coup, and has had it extended several times. With this status, it has been able to carry out a widespread purge that has shaken up just about every aspect of public life in Turkey.

Erdogan has been widely criticized for the purge by Western leaders, who accuse him of taking on a dictatorial role. They also condemned his recent referendum win to change the constitution, which could essentially see him leading the country until as late as 2029.

But Trump was one of the first leaders to get on the phone and congratulate Erdogan for his victory, so it is unclear whether he will express any concerns over the development.