The EU's foreign ministers have urged Turkish President Tayyip Erdogan to respect the rule of law in dealing with coup plotters - and warned him against reinstating the death penalty.

Ministers condemned the weekend coup but expressed alarm at Erdogan's public comments on Sunday that there could be no delay in using capital punishment.

Their warning came as the US urged all parties to show restraint and act within the rule of law after the failed plot.

'The United States strongly supports Turkey's democratically elected civilian government and that country's democratic institutions,' White House spokesman Josh Earnest said at a news briefing.

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President Tayyip Erdogan ordered F-16s to patrol the skies over Turkey following a failed coup

Earlier, foreign ministers from across the EU has said in a statement: 'The EU recalls that the unequivocal rejection of the death penalty is an essential element of the union acquis.'

The statement was agreed by all 28 EU ministers, including Boris Johnson, attending his first EU Foreign Affairs Council in Brussels.

Germany, Austria and France also warned separately that bringing back the death penalty, which Turkey abolished in 2004, would undo years of membership talks that began in 2005.

Reintroduction of the death penalty would prevent successful negotiations to join the EU,' said German Foreign Minister Frank-Walter Steinmeier, a position echoed by his French counterpart Jean-Marc Ayrault in less direct terms.

Meanwhile, EU foreign policy chief Federica Mogherini warned the Turkish government against taking steps that would damage the constitutional order following a failed weekend coup, as F-16 fighter jets patrolled Turkey's skies and the military carried out fresh raids.

EU foreign policy chief Federica Mogherini (pictured with US Secretary of State John Kerry) warned the Turkish government against taking steps that would damage the constitutional order

'We were the first... during that tragic night to say that the legitimate institutions needed to be protected,' she told reporters on Monday on arrival at an EU foreign ministers meeting, which was also to be attended by U.S. Secretary of State John Kerry.

'We are the ones saying today rule of law has to be protected in the country,' she said in Brussels. 'There is no excuse for any steps that takes the country away from that.'

She also said: 'The democratic and legitimate institutions needed to be protected. Today, we will say together with the ministers that this obviously doesn't mean that the rule of law and the system of checks and balances does not count.'

'On the contrary, it needs to be protected for the sake of the country itself. So we will send a strong message.'

Other ministers also expressed concerns about events after the coup. Mogherini's fellow EU commissioner, Johannes Hahn, who is dealing with Turkey's membership request, said he had the impression that the government had prepared lists of those such as judges to be arrested even before the coup took place.

'It looks at least as if something has been prepared. The lists are available, which indicates it was prepared and to be used at a certain stage,' Hahn said. 'I'm very concerned. It is exactly what we feared.'

Belgian Foreign Minister Didier Reynders said he was also concerned about the arrests of judges and also about President Tayyip Erdogan's suggestion of reintroducing the death penalty for plotters. That, Reynders said, 'would pose a problem with Turkey's ties with the European Union'.

The coup plotters sent warplanes firing on key government installations and tanks rolling into major cities. Pictured are workers inspecting the Grand National Assembly, which was bombed by rebel jets

Abolishing capital punishment, as Turkey did in 2004 before it could open the formal process of accession negotiations with the EU, is a prerequisite for holding talks on membership.

Reynders said: 'We cannot imagine that from a country that seeks to join the European Union. We must be very firm today, to condemn the coup d'etat but the response must respect the rule of law.

French Foreign Minister Jean-Marc Ayrault said: 'We cannot accept a military dictatorship but we also have to be careful that the Turkish authorities do not put in place a political system which turns away from democracy ... The rule of law must prevail ... We need authority but we also need democracy.'

Meanwhile, NATO's chief this afternoon joined others in calling for Turkey's leadership to respect the rule of law.

'I have spoken to President Recep Tayyip Erdogan in the aftermath of the attempted coup in Turkey,' NATO Secretary-General Jens Stoltenberg said Monday in a statement.

'I welcomed the strong support shown by the people and all political parties to democracy and to the democratically elected government. The Turkish people have shown great courage.'

As he did early on Saturday, Stoltenberg condemned the attempted coup in Turkey and reiterated his full support for Turkey's democratic institutions.

'Being part of a unique community of values, it is essential for Turkey, like all other allies, to ensure full respect for democracy and its institutions, the constitutional order, the rule of law and fundamental freedoms,' the NATO chief said.

The EU's Foreign Ministers condemned the weekend coup attempt, but expressed alarm at public comments by Erdogan (pictured) that there could be no delay in using capital punishment

He called Turkey a 'valued NATO ally,' and offered his condolences to the families of the innocent people who lost their lives in the takeover attempt.

In a sign that authorities fear that the threat against the government is not yet over, warplanes continue to patrol the skies over Turkey.

A senior official, speaking anonymously, said on Monday that F-16 jets guarded the Turkish airspace overnight. Turkey also carried out fresh raids.

Judges and military commanders are among 6,000 people who were arrested over the weekend.

The coup plotters sent warplanes firing on key government installations and tanks rolling into major cities, but the rebellion was quashed by loyal government forces and masses of civilians who took to the streets. At least 294 people were killed and more than 1,400 wounded.

The state-run news agency, Anadolu, said Erdogan ordered the overnight patrol by F-16s.