President Recep Tayyip Erdogan has lashed out at Turkey's Western allies over last month's failed putsch, accusing them of supporting "terror" and demanding Washington extradite a preacher he says orchestrated the coup.

Erdogan, who blames the attempt to unseat him on US-based preacher Fethullah Gulen, described the July 15 coup as a "scenario written from outside" in an allusion to foreign involvement.

And he lashed out at the United States for dragging its heels over Ankara's request to extradite him, describing it as "a huge obstacle" to Turkey's fight against terror.

Since the putsch, Erdogan has pursued a relentless crackdown, detaining more than 18,000 people and firing tens of thousands of others, with the latest sweep hitting Turkey's football association and medical staff at Ankara's military hospital.

The purge has set alarm bells ringing in the West, which has voiced growing concern over the scope of the operation, drawing a fierce response from Erdogan.

"Unfortunately, the West is supporting terror and standing by the coup plotters," Erdogan said in a typically combative speech at his presidential palace, denouncing "those who we imagined to be friends".

He lashed out at Germany's judicial authorities for not allowing him to address by video link a weekend rally supporting him in Cologne, saying Berlin had previously permitted leaders from the outlawed Kurdistan Workers Party (PKK) to do so at earlier events.

And he all but accused foreign powers of having a hand in drawing up the putsch, which was carried out by a rogue faction within the military.

"This coup was not just an event planned from the inside. The actors inside acted out a scenario for a coup written from the outside," Erdogan said.

- 'A huge obstacle' -

Addressing Washington over Gulen, he asked: "How can it be, when we are strategic partners... you keep on hiding and sheltering him?"

And in a television interview with Mexico's Televisa, he accused Washington of dragging its feet over his extradition by asking for documents.

"You have to be blind and deaf not to understand that he is behind all of this," he said.

"If we request the extradition of a terrorist then you should fulfil that," he said.

"If you start asking for documents and what not, then it's a huge obstacle in our way of fighting terrorism."

US Secretary of State John Kerry said on July 18 that Turkey must present "genuine evidence" and "not allegations" against the Muslim cleric for his extradition.

The failed putsch has aggravated already-strained ties between the two NATO allies with some government ministers even alleging Washington could have had a hand in the plot, something US officials have dismissed as "ludicrous".

In Ankara, police on Tuesday rounded up some 50 staff, including doctors, at Gulhane Military Medical Academy (GATA) hospital, the state-run Anadolu news agency reported, quoting police sources.

Speaking on condition of anonymity, a Turkish official told AFP warrants had been issued for the detention of 98 staff suspected of helping fast-track Gulen supporters into the military through favourable medical reports.

It was the first time a medical establishment has been targeted in a clampdown under a three-month state of emergency that has also hit journalists and academics.

Turkey's football federation meanwhile confirmed it had fired 94 officials including referees and assistant referees.

As Western concern grows over human rights in Turkey, the head of the Council of Europe, a top European rights watchdog, was due to begin a two-day visit later Wednesday, including a meeting with Erdogan.

- 'Gulen, a flight risk' -

Ankara has also staged a sweeping overhaul of state institutions, sacking tens of thousands of civil servants, with Prime Minister Binali Yildirim saying the government was engaged in "virus and traitor cleansing" to weed out Gulenists from state institutions.

Another 36 people were detained over a sex tape scandal that felled the leader of the main opposition party in 2010, with prosecutors linking the affair to Gulen.

Gulen, who has lived in self-imposed exile in the United States since 1999, has denied any involvement in the attempted putsch.

Turkey's Justice Minister Bekir Bozdag on Tuesday confirmed sending a new package of Gulen-related documents to Washington, saying: "He needs to be arrested urgently as we have intelligence that he might flee to a third country."

Turkey has said the coup could cost its economy up to $100 billion ($89 billion euros) overall.