The altercation occurred Tuesday afternoon as supporters and opponents of the visiting president clashed at the residence, which is located about half a mile away from the Turkish Embassy in the US capital, authorities said.
Erdogan called Trump his "dear friend" and made a point to congratulate the USA president on his "legendary triumph" over Hillary Clinton in the 2016 presidential election.
Violence broke out Tuesday during a protest in front of the Turkish embassy in Washington, DC's Embassy Row, leaving at least nine people injured in what quickly turned into an all-out brawl.
Videos from Tuesday's protests in Washington, some of which were posted on the internet, showed people from both sides shouting and being punched with each side accusing the other of being the aggressors.
"They think they can engage in the same sort of suppression of protest and free speech that they engage in in Turkey", Arthur said.
The victims were transported to George Washington University Hospital.
"We look forward to having a long and productive discussion", Trump said.
Despite Trump's praise, relations with the U.S. and Turkey have been strained of late, and Erdogan brought a laundry list of complaints about American policies with him to Washington. Trump said it was a "great honor" to host Erdogan.
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The PKK has fought an insurgency in south eastern Turkey since 1984 and is considered a terrorist group by the United States, Turkey and Europe.
Still, the Turkish president made it clear the Trump administration's decision to arm one group of Syrian Kurds fighting the Islamic State, the YPG, would "never be accepted".
Ankara regards the YPG as simply the Syrian arm of the "terrorist" PKK, which has waged a deadly insurgency inside Turkey since 1984, and Erdogan is anxious his deadly enemy will find itself in charge of a USA -armed statelet on his southern frontier.
The United States sees the YPG as distinct from the PKK and as a valuable partner in the fight against Islamic State. 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.
However, Trump avoided such issues and instead praised the efforts of Turkey to fight against internal "terrorists" as well as their fight against ISIS militants.
"President Erdoğan and I are also discussing the need to reinvigorate our trade and commercial ties".
"Human rights and democracy are not part of Trump's agenda, but we hope that he abandons this stance", Tanrikulu said.
Secretary of Defense James Mattis also met with Turkish Minister of Defense Fikri Işık today at the White House.