Turkish President Recep Tayipp Erdoğan says he returned a letter to Donald Trump in which the president told him not to be a "fool" and a "tough guy" before Turkey launched an assault on allied Kurdish forces in Syria.

Mr Trump's 9 October letter warned history will "look upon you forever as the devil" should Turkey proceed with its offensive.

Mr Erdoğan revealed he returned the letter after a meeting between the two leaders on Wednesday, weeks after Turkey moved its military into northern Syria following the withdrawal of US troops from the region. The president invited Mr Erdoğan to the White House, joined by a host of Republican Senators.

But the leaders appeared at odds, with the Turkish president comparing Kurdish forces allied with the US in Syria to "terrorists" and blaming Turkish cleric Fethullah Gulen, who lives in the US, for a 2016 coup. The US has refused to extradite Mr Gulen, and Mr Trump has said that it's "not under consideration".

Mr Erdoğan also addressed a Turkish reporter who asked Mr Trump to explain why he had invited a Kurdish military leader and "terrorist" to the White House.

Turkey launches offensive into Syria Show all 25 1 /25 Turkey launches offensive into Syria Turkey launches offensive into Syria Turkish soldiers with armored vehicles EPA Turkey launches offensive into Syria A woman flees with her children during Turkish bombardment on Syria's northeastern town of Ras al-Ain AFP/Getty Turkey launches offensive into Syria Smoke billows following Turkish bombardment on Syria's northeastern town of Ras al-Ain in the Hasakeh province along the Turkish border on October 9, 2019. - Turkey launched an assault on Kurdish forces in northern Syria with air strikes and explosions reported along the border. President Recep Tayyip Erdogan announced the start of the attack on Twitter, labelling it "Operation Peace Spring". (Photo by Delil SOULEIMAN / AFP) (Photo by DELIL SOULEIMAN/AFP via Getty Images) DELIL SOULEIMAN AFP/Getty Turkey launches offensive into Syria The first group of Turkish infantry prepare to enter Syria on the border Getty Turkey launches offensive into Syria Civilians flee AFP/Getty Turkey launches offensive into Syria Smoke billows from targets inside Syria AP Turkey launches offensive into Syria Turkish armoured vehicles enter Syria in Akcakale Getty Turkey launches offensive into Syria Civilians leave as smoke rises from Ras al-Ain AFP Turkey launches offensive into Syria A multi-rocket launcher fires in an unknown location Turkish Defence Ministry via Reuters Turkey launches offensive into Syria People wave as Turkish soldiers prepare to cross the border Getty Turkey launches offensive into Syria Girls stand together in Ras al Ain town Reuters Turkey launches offensive into Syria A woman walks as smoke billows following Turkish bombardment in Syria's northeastern town of Ras al-Ain AFP/Getty Turkey launches offensive into Syria A Turkish army's tank drives down from a truck towards the border with Syria AFP/Getty Turkey launches offensive into Syria Turkish jet taxis on tarmac after returning to a military base in southeast Diyarbakir Reuters Turkey launches offensive into Syria A Turkish armored vehicle drives down a road during a military operation in Kurdish areas of northern Syria EPA Turkey launches offensive into Syria People sit on belongings at a back of a truck as they flee Ras al Ain town Reuters Turkey launches offensive into Syria Turkey-backed Syrian opposition fighters enter Tel Abyad AFP/Getty Turkey launches offensive into Syria Civilians flee AFP/Getty Turkey launches offensive into Syria People flee Tal Abyad North Press Agency/Reuters TV Turkey launches offensive into Syria People wave as Turkish soldiers prepare to cross the border into Syria Getty Turkey launches offensive into Syria Civilians flee with their belongings AFP/Getty Turkey launches offensive into Syria Civilians flee during Turkish bombardment on Syria's northeastern town of Ras al-Ain in the Hasakeh province along the Turkish border on October 9, 2019. - Turkey launched a broad assault on Kurdish-controlled areas in northeastern Syria today, with intensive bombardment paving the way for an invasion made possible by the withdrawal of US troops. (Photo by Delil SOULEIMAN / AFP) (Photo by DELIL SOULEIMAN/AFP via Getty Images) DELIL SOULEIMAN AFP/Getty Turkey launches offensive into Syria Turkish President Recep Tayyip Erdogan, right, speaks with Defense Minister Hulusi Akar, left, as they watch the operation by Turkish forces in Kurdish areas EPA Turkey launches offensive into Syria Smoke rises from the Syrian town of Tal Abyad AFP/Getty Turkey launches offensive into Syria Turkey-backed members of Syrian National Army prepare for moving to Turkey with heavy armed vehicles EPA

The Turkish-backed Syrian National Army has been accused of sweeping violence across northern Syria, including civilian attacks, kidnappings and summary executions, while the Turkish military has targeted Kurdish troops who helped US troops defeat Isis in the region.

But Mr Erdoğan, speaking next to Mr Trump, accused the US-backed YPG of falling under the umbrella of terror-linked group PKK and "attacking our soldiers and civilians in a very provocative manner". He suggested "empathetic" reports are "using information to cloud ... public perception with the eventual gain or goal of harming our relations".

The Trump administration is legally bound to impose sanctions against Turkey for its purchase of a Russian missile defence system, but Mr Trump has pleaded with his Republican allies to ease tensions to smooth a $100 billion two-way trade deal between the two countries.

He said Turkey's acquisition of Russian weapons "created some very serious challenges for us" but the leaders are talking about it "constantly".

"Hopefully we'll be able to resolve that situation," he told reporters at the White House.

Mr Trump wrote to Mr Erdoğan that despite the country obtaining Russian anti-aircraft weapons and a Congressional resolution to impose sanctions against Turkey for its assault in Syria, Mr Trump told reporters at the White House this morning that the US "can be doing $100 billion with Turkey and right now we're doing about $20 billion. But we think that number should be easily $100 billion, which would be great for Turkey and great for us."

Mr Erdoğan told reporters that Congress had "cast a deep shadow" over relations between the two countries. Last week, the House voted to define the early 20th century massacre of Armenians by Ottoman forces as a "genocide".

The accelerated withdrawal of US troops from Syria paved the way for a Turkish invasion of Kurdish-controlled areas in the country, which has ceded control of the destabilised area and its allied forces to Iran and Russia as well as neighbouring Turkey.

Mr Trump told reporters earlier that "it's time not to be worried about other peoples' borders" but pledged to keep troops in the area to secure oil fields. "We left troops behind only for the oil", he said.

Last month, Vice President Mike Pence met Mr Erdoğan to help negotiate a ceasefire in Syria.

US troops guard Syrian oil fields

Asked whether Turkey plans to repair relations with Kurds in the region, Mr Trump said the US "has as great relationship with the Kurds".

"We fought together", he said. "Many Kurds live in Turkey and are happy and well taken care of ... That's really a misnomer."

But Mr Erdoğan made the distinction between Kurds and "terrorist organisations" he has accused of killing hundreds of people and injuring thousands others. "Whoever they might be, but we have to make a distinction here", he said. "We're just fighting terrorists, period."

Democratic Senator Chuck Schumer told the Senate on Wednesday that "the fact that President Trump rewarded Erdoğan with an Oval Office meeting today is mind boggling".

Syrian president Bashar al-Assad praises Donald Trump's 'transparency'

In 2015, Mr Trump admitted a "little conflict of interest" in his dealings with Turkey. Mr Trump has often been accused of using the office as leverage for private business; the president has not completely removed himself from the Trump Organisation, which collects licensing fees for the use of Mr Trump's name on its buildings. As then-prime minister, Mr Erdoğan cut the ribbon at Istanbul's Trump Towers in 2012.

Mr Erdoğan also is embroiled in a US lawsuit over Halkbank, a Turkish state-owned bank that the Southern District Court of New York has accused of helping move $20 billion to Iran, violating US sanctions against that country.

Protests erupted outside the White House during Mr Erdoğan's previous visit to Washington in 2017, when Mr Erdoğan's guards attacked protesters including women and elderly men, as well as members of a US security detail, outside a Turkish ambassador's residence.

More than a dozen guards accused of inciting violence had already left the country before they were charged, though the charges against most of the crew were dropped.

Recently released State Department documents as part of a lawsuit against Turkey on behalf of victims revealed that Mr Erdoğan's guards were quickly escorted to Joint Base Andrews by State Department diplomatic security and Secret Service.