Washington (CNN) President Donald Trump, in hosting Turkey's President Recep Tayyip Erdogan at the White House Tuesday, extended his latest warm welcome to an authoritarian-style leader who had a strained relationship with the previous US administration.

"The American and Turkish peoples have been friends and allies for many, many decades," said Trump, as he stood beside Erdogan to deliver remarks after their oval office meeting.

"We support Turkey in the fight against terror groups like ISIS and the PKK, and ensure they have no safe quarter," he added. "We also appreciate Turkey's leadership in seeking an end to the horrific killing in Syria."

Despite the apparent warmth between the two leaders, relations have been strained by the US refusal to extradite a Turkish cleric living in Pennsylvania whom Erdogan blames for orchestrating a July coup attempt against him.

And the two countries are at odds over Trump's decision to arm Kurdish militias that are helping in the fight to rout ISIS from its Syrian stronghold in Raqqa. Turkey sees these militias, which are widely seen as the most effective fighting force on the ground, as an extension of the outlawed Kurdistan Workers Party, or PKK, which is considered a terrorist group in the US, Turkey and Europe.

Standing beside Trump, Erdogan said that Turkey would not consider any plans for Kurdish groups to be part of the region's future.

"There is no place for the terrorist organization in the future of our region, taking YPG and PYD into consideration in the region will never be accepted and it's going to be against a global agreement that we have reached," President Erdogan said.

As well as congratulating Trump on his election victory, Erdogan stressed the importance of US-Turkey cooperation."The relations between Turkey and the United States have been erected upon common democratic values and common interests," said Erdogan. "Keeping our outstanding relations stronger than ever will be very important not only for our common interests, but also stability of the globe and peace around the world."

Erdogan sought use the visit as a means of underscoring a new era in close US-Turkey ties, in fighting terrorism as well as building economic and trade opportunities, saying that he was "determined to expand relations."

"I believe my current official visit to the United States will mark a historical turn" said Erdogan, adding that he hoped to "enjoy some further gains in terms of the future."

But he didn't pass up the opportunity to register his unhappiness about the cleric Fethullah Gulen , now living in Pennsylvania. The Turkish leader said that he had been "frankly communicating" Turkey's expectations with regard to the organization, and had "notified our friends" about Gulen's alleged involvement in the last year's attempted coup.

Erdogan was in Washington to try to convince the US President to reverse the decision to arm the Kurdish fighters and to brief Trump on a proposed peace plan for Syria that Ankara has reached with Russia and Iran, and involves the creation of four de-escalation zones within the country.

Turkey, a NATO member, is a vital ally in the fight against ISIS, allowing the US to use its Incirlik air base in the fight against the terror group. Relations were strained, if businesslike, for the last few years as the Obama administration distanced itself from Erdogan's increasingly authoritarian rule.

A bipartisan group of lawmakers wrote Trump Tuesday to ask him to raise human rights with Erdogan, given the increasing repression in his country. They cited the weakening of democratic institutions, stifling of fundamental human rights, mass arrests and civil society restrictions that have been taking place even before a constitutional referendum in April gave Erdogan increased powers and extended his time in office.

"Erdogan and his allies have mounted an assault on the rule of law, particularly using sweeping state of emergency authorities to stifle fundamental rights including free speech, undermine the independence of the judiciary, and quash any opposition to their undemocratic actions," said the letter signed by Florida Republican Sen. Marco Rubio, New Jersey Democratic Sen. Robert Menendez and 15 others senators.

JUST WATCHED CNN exclusive with Turkey's President Erdogan Replay More Videos ... MUST WATCH CNN exclusive with Turkey's President Erdogan 20:37

Trump didn't touch on any of the disagreements and instead praised Turkey's efforts in the war against ISIS and for its fight against internal terrorist attacks. He stressed that the US would "offer our support to Turkey" in its fight against terrorism and that they would "reinvigorate our trade and commercial ties."

"These are areas where we can rebuild our relationship," Trump said in comments earlier in the day.

A short official readout of the two leaders' meeting further reiterated their efforts to work together in combating terrorism "in all its forms" and the "deep and diverse relationship" between the two nations. It also referenced the i ncarceration of US national, Andrew Brunson , an evangelical Presbyterian pastor from North Carolina, who is currently detained in Turkey. Trump, the readout claimed, asked that the Turkish Government "expeditiously return him to the United States."

Trump was one of very few world leaders who called Erdogan to congratulate him on winning the referendum, which was preceded by widespread arrests of his opponents and was so narrowly won that many questioned its legitimacy.

All Trump's interactions with Erdogan are overshadowed by his family's business holdings in the country. In a 2015 interview with Breitbart News, Trump told Steve Bannon -- now his adviser -- that "I have a little conflict of interest because I have a major, major building in Istanbul."

During the presidential campaign, when Trump was calling for a ban on Muslims entering the country and floating the idea of a Muslim registry, Erdogan called for the then-candidate's name to be removed from Istanbul's Trump Towers, saying Trump had "no tolerance for Muslims."

In a separate meeting at the White House, Secretary of Defense Jim Mattis, met with his Turkish counterpart, Minister of Defense Fikri Isık. According to a readout of the meeting provided to the press by the pentagon, the two men discussed efforts to combat the PKK, and the crisis in Syria.