"With regard to the question of possible involvement in the coup attempt by persons residing in the United States - we have been clear that the United States would be willing to provide assistance to Turkish authorities conducting their investigation into the coup attempt", Bass said. He has shaken up the government, cracked down on dissent, restricted the media and renewed fighting with Kurdish rebels.
Erdogan has blamed a high-profile former ally who has since become a bitter rival, Fethullah Gulen, for the attempt.
Their cooperation was at its best - and worst - when Gulenists in the press and judiciary, along with the Erdogan government, conducted two weird show trials over five years that rounded up hundreds of military officers, intellectuals, university presidents, women's rights advocates, and writers.
"This is no excuse to take the country away from fundamental rights and the rule of law, and we will be extremely vigilant on that", European Union foreign policy chief Federica Mogherini said at a joint news conference with U.S. Secretary of State John Kerry.
Though government officials offered reassurances that life has returned to normal, warplanes patrolled Turkey's skies overnight in a sign that authorities feared that the threat was not yet over.
Meanwhile, a Greek court will decide on Thursday the fate of eight Turkish military officers who fled across the border by helicopter after the failed coup in Turkey and who Ankara wants to see extradited.
The detained suspected military coup plotters included arrested 103 generals and admirals, state media said, while almost 3 000 judges and prosecutors were dismissed in the wake of the weekend's events. Akin Ozturk of being the ringleader of the coup, though he told prosecutors he did not plan or direct it.
The French foreign minister, Jean-Marc Ayrault, said Turkey was a "strategic partner" but had to respect fundamental liberties.
Before his detention, Ozturk had denied in a statement that he was involved in the uprising, insisting that he had worked to quash it.
Mr Yildirim said 232 people were killed in Friday night's violence: 208 of them were civilians, police and loyalist soldiers, and a further 24 were coup plotters.
As pro-coup forces were rounded up over the weekend, there were parades of religious zealots in the streets chanting "Allahu Akbar" as giant speakers in Taksim Square in central Istanbul blasted out verses from the Koran. Searches for suspects continued in several cities and on Monday a man was killed outside an Ankara courthouse after reportedly firing on security forces. It was not clear if any arrests were made.
Thanks to the Gulen uproar, Turkish media are filled with anti-American conspiracy theories charging Washington with endorsing the plot - a charge even some of Erdogan's cabinet ministers are making.
The coup crumbled after President Tayyip Erdogan, on holiday at the coast, phoned in to a television news programme and called for his followers to take to the streets. He had indicated a shake-up of the military was imminent and had also taken steps to increase his influence over the judiciary.
Deputy Prime Minister Numan Kurtulmus defended the crackdown on judiciary officials in an interview with CNN-Turk, saying many of them would have played a role had the coup attempt succeeded.
"We were the first. during that tragic night to say that the legitimate institutions needed to be protected", she told reporters on arrival at the European Union foreign ministers meeting.
When asked what he would do if the United States refused to extradite Gulen, he said "we have a mutual agreement of extradition of criminals".
Soldiers suspected of being involved in the coup attempt are escorted by policemen as they arrive at a courthouse in the resort town of Marmaris, Turkey, July 17, 2016.
At the White House, spokesman Josh Earnest stressed US support for Turkey's "democratically elected" government and said Washington strongly values "the important relationship" with its North Atlantic Treaty Organisation ally.
"NATO will indeed measure very carefully what is happening and my hope is that Turkey is going to move in ways which do respect what they have said to me many times is the bedrock (value) of their country", Kerry said.
Following the failed coup, some politicians have advocated reintroducing the death penalty, which Turkey abolished in 2004, after joining a binding Council of Europe treaty that prohibits it.