U.S. President Donald Trump pushed Turkish President Recep Tayyip Erdogan to walk away from the purchase of a Russian missile defense system on Wednesday, but declared himself "a great fan" of his counterpart and said they had a "wonderful and productive" encounter.

Was there progress on S-400?

Trump and Erdogan fell short of explaining in concrete terms how they would overcome the mounting differences they have on numerous issues such as Syria policy and Turkey's purchase of the Russian S-400 missile defense system.

"Turkey's acquisition of sophisticated Russian military equipment, such as the S-400, creates some very serious challenges for us and we are talking about it constantly," Trump told a joint news conference, adding, "Hopefully we'll be able to resolve that situation.”

The White House later released a statement using firmer language. "In order to achieve progress on other fronts, it is vital that we resolve the issues involving Turkey's purchase of the Russian S-400 air defense system, strengthening our defense partnership," it said.

Turkey and the United States have been at loggerheads over the purchase of the S-400 system, which the United States says is not compatible with NATO defenses and poses a threat to Lockheed Martin's F-35 "stealth" fighter jet.

Turkey had shrugged off threats of U.S. sanctions and began receiving its first S-400 deliveries in July. To punish Turkey for its purchase, the United States has banned sales of F-35s to Turkey and removed the country from a multinational program to produce the warplane.

Erdogan said that the two countries could only overcome their dispute on the S-400s and F-35s through dialogue. "We have agreed to open a new page in our relationship," he said.

How did the meeting go?

Despite the tensions on policy issues, Trump gave a warm welcome to Erdogan. It was in sharp contrast to anger in the U.S. Congress over Ankara's offensive into Syria to drive out a Kurdish militia that has been Washington's main partner in the fight against ISIL.

"We've been friends for a long time, almost from Day 1. We understand each other's country. We understand where we are coming from," Trump told Erdogan as they sat next to each other in the Oval Office.

Trump added that he wants to seal a two-way trade agreement with Turkey to increase bilateral trade to as much as 1 billion U.S. dollars.

The two countries, which boast the two largest armies in NATO, hit a crisis point last month when Erdogan began his cross-border incursion against America's Kurdish allies in Syria and upended the U.S. presence there.

Erdogan was critical of a House of Representatives vote last month in favor of a non-binding resolution recognizing the killings of 1.5 million Armenians a century ago as a genocide, a symbolic but historic vote denounced by Turkey.

The Turkish president said he was "hurt deeply" by the resolution and warned it could cast a "deep shadow over our bilateral relations."

(With input from Reuters)