US Secretary of State John Kerry says the United States and the European Union (EU) will continue their “unbreakable” partnership in the light of Britain’s departure from the bloc and the security challenges that Europe faces.

During a joint press conference on Monday with EU foreign policy chief Federica Mogherini in Brussels, Kerry said Washington was working with the EU and UK to arrange “the smoothest possible transition” for Britain to exit the EU.

He said the Brexit decision has given more significance to the Transatlantic Trade and Investment Partnership (TTIP) trade deal between the US and the EU.

US President Barack Obama had hinted earlier that the two sides will proceed with the controversial deal and negotiations will remain unaffected by London’s move.

Kerry echoed that view in his remarks, stating that the deal would mitigate damages caused by Brexit.

The treaty has "a very significant ability to act as a counter to whatever negatives may or may not ultimately attach themselves to whatever construct is negotiated between the UK and Europe," Kerry said.

The top US diplomat then touched on the recent attempted coup in Turkey, urging Turkey to respect the rule of law in punishing the plotters.

Mogherini also chimed in on the issue, warning Ankara that reinstatement of the death penalty would spell the end to Turkey’s years-long bid to join the EU.

The botched coup began late on July 15, when a faction of the Turkish military blocked Istanbul’s iconic Bosphorus Bridge and attacked the headquarters of the Turkish intelligence agency and parliament in the capital.

Turkey’s President Recep Tayyip Erdogan hinted on Sunday that the country may reintroduce the death penalty to allow the execution of those involved in the failed coup.

At least 6,000 people have been arrested across the country after the failed coup and the crackdown is expected to be widened, Justice Minister Bekir Bozdag said on Sunday.

Turkey has also urged the US to extradite opposition figure Fethullah Gulen for orchestrating the coup, an allegation Gulen has firmly rejected.

Kerry said Monday that the extradition request will only be processed when Turkey provides genuine evidence that withstands scrutiny.

"The US has a formal process for dealing with extradition requests, Turkey must send evidence not allegations," he said.