After the swearing-in held in parliament, Erdogan's inauguration ceremony took place at the presidential palace here with dozens of foreign heads of state and high-ranking officials attending the event.
After the ceremony, 29 North Atlantic Treaty Organisation heads of state and government also visited an exhibition on the organization's history and activities along with Stoltenberg. "We are leaving behind the system that has in the past cost our country a heavy price in political and economic chaos".
Empowered by a popular mandate on the back of a convincing electoral victory, Erdoğan will have to address urgent questions in Turkey such as the fate of more than 3 million Syrian refugees living in the country, the progress of the war across the border, a faltering economy and a weakening currency.
Erdogan pledged to "reinforce the social state" in the new era and "leave behind the days that people were externalized and alienated for whatever reason".
The new system abolishes the post of prime minister, granting the president the power to appoint the cabinet - which he was expected to announce later on Monday - and unelected vice-presidents. Previously, the prime minister formed the government by making elected members of parliament ministers. "It is a sign that Erdogan will control economic policy even more", said Guillaume Tresca, a senior emerging markets strategist at Credit Agricole.
The president now sits at the top of a vertical power structure marked by a slimmed-down government with 16 ministries instead of 26 and multiple bodies reporting to him.
Under his leadership Ankara started accession talks with the European Union, which stalled amid EU criticism of Turkey's human rights.
Erdogan named his son-in-law Berat Albayrak as treasury and finance minister in an updated cabinet that excluded former deputy prime minister Mehmet Simsek, seen as the main market-friendly minister in the previous government.
Foreign Minister Mevlut Cavusoglu, Interior Minister Suleyman Soylu and Justice Minister Abdulhamit Gul have retained their portfolios in the new cabinet.
Armed forces chief of staff Hulusi Akar was named defence minister.
Mr Erdogan is now the country's most powerful leader since Ataturk: modern Turkey's secular founding father, who saw Turkey as part of the west.
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"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.
In a speech on Saturday, Erdogan said he would tackle high-interest rates, inflation and a wide current account deficit.
In his message, the King said that "this re-election is a testament to the renewed confidence of the Turkish people" in the president's efforts "to advance, develop and strengthen Turkey's position" internationally.
Erdogan will visit two traditional allies this week - Azerbaijan and Turkish northern Cyprus.
After the summit in Brussels, Trump was to stay for three days in the United Kingdom - where massive protests were expected.
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