Trump and Erdogan - who on Monday put his son-in-law in charge of a new combined ministry of treasury and finance, further solidifying his power - were among the last to take the stage for the group photo. "Turkey is leaving behind a system which cost the country politically, socially and economically".
Armed forces chief of staff Hulusi Akar was named defence minister.
Foreign Minister Mevlut Cavusoglu, Interior Minister Suleyman Soylu and Justice Minister Abdulhamit Gul have retained their portfolios in the new cabinet.
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Some 30,000 people will gather in London's Hyde Park to watch the game, with the Lightning Seeds set to perform Three Lions before kick-off.
On the eve of Monday's inauguration authorities dismissed more than 18,000 state employees - majority from the police and army - in what the government said would be the final decree under emergency rule imposed following a failed 2016 coup.
After the swearing-in ceremony, Mr Erdogan visited the mausoleum of the founder of the Turkish Republic, Mustafa Kemal Ataturk before proceeding to the Presidential Complex to make his inaugural speech.
"We are facing a period where we have to work hard to bring inflation down to single digits again", said Albayrak, adding that Turkey will have a stronger monetary policy in the upcoming period. As head of the executive branch, Erodgan will have the power to issue decrees with the force of law, prepare the budget subject to parliament's approval, dissolve parliament and call for new presidential and parliamentary elections, and appoint high-level officials, including ministers and some top judges.
"Most powers will be concentrated in his hands, there will no longer be a prime minister, and nearly none of the checks and balances of liberal democracies will be present".
"Albayrak was one of 16 ministers named in the new streamlined cabinet after the ceremony at the presidential palace, which state news agency Anadolu said was attended by Venezuelan President Nicolas Maduro, Russian Prime Minister Dmitry Medvedev and Sudanese President Omar Hassan al-Bashir, who is wanted for war crimes by the International Criminal Court".
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Meanwhile, Prince Harry's brother wore his traditional uniform as he attended the service to mark 100 years of the RAF. The Duchess of Sussex opted for a neutral palette with her Roland Mouret dress and black Fendi bag.
No major Western leader featured on a list of 50 presidents, prime ministers and other high-ranking guests. In 2016, a coup to depose him failed. "It is a sign that Erdogan will control economic policy even more", Guillaume Tresca, a senior strategist at French bank Credit Agricole, told Reuters.
The new government faces immediate economic challenges.
Erdogan faces economic problems such as high interest rates and inflation as well as a plunging currency that has lost 17 percent of its value against the dollar since the start of 2018.
Turkey also faces a widening current account deficit making it reliant on weak foreign investment to plug the gap.
"When you scrap the five-year term you remove this shield", he said. Erdogan, the AK Party and MHP candidate, won the June 24 presidential election with 52.5 percent of the vote.
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A vehicle seized by men in camouflage gear and gas masks belongs to a paramedic and RAF hero who treated Ms Sturgess, locals say. Both Skripals have recovered from the poisoning and a police investigation into the incident is ongoing.