The D.C. police chief said, "There could be a diplomatic immunity issue, but that won't prevent us from doing what we need to do."
New videotape emerges of the Turkish president apparently watching the brawl from inside his car.
Police said that nine people were injured and one is in a critical condition.
At the White House meeting, Trump lauded Erdogan as an important ally in the "fight against terrorism."
The warning came a week before Turkey's president is due to visit Washington.
The ban came after two site entries accused Turkey of links to Islamist militant groups.
The Turkish leader earlier urged more Muslims to visit the city to support the Palestinians' claim to contested site.
It's only a matter of time before a Turkish soldier shoots an American in defense of Turkey's honor.
Populism is proof of the clash between a globalized world and national democracies.
Turkey and India's leaders pledged tightening economic and counterterrorism ties.
To an authoritarian, rules that block what he wants to do are always "bad for the country."
Turkish nationalist Sedat Peker has suggested Turkey should kill the presidents of European countries that defy Erdogan.
The European Union has warned that reintroducing capital punishment would end Turkey's bid to join the bloc.
Whichever way the vote goes on Sunday, women in Turkey stand to lose the freedoms they've enjoyed for years.
Authorities said explosives in a tunnel causes the blast in the city of Diyarbakir, killing a police officer and two civilians.
Turkish President Recep Tayyip Erdogan said "Operation Euphrates Shield" was over, but Ankara had "good surprises" in store for the Islamic State group and Kurdish militants in Syria and Turkey.
The Turkish leader has repeatedly lashed out at European countries while campaigning for votes in a referendum to increase presidential powers.