In a phone call, Palestinian President Mahmoud Abbas also congratulated Erdogan on "the success of the Turkish democratic process and his victory in the presidential elections", said the official Palestinian News Agency (WAFA). "We will embrace everyone", he said.
"Our people have given us the duty of carrying out the presidential and executive posts,"he said in a short televised speech, citing unofficial results".
The president has for the last two years ruled under a state of emergency imposed in the wake of the 2016 failed coup, with tens of thousands arrested in an unprecedented crackdown which cranked up tensions with the West.
Under constitutional amendments approved after a controversial 2017 referendum, Turkey is making a transition from a parliamentary system to a presidential one - giving the next president expanded powers, abolishing the prime minister's post, and eliminating numerous checks and balances created to help parliament protect against the misuse of presidential powers.The changes will take effect after the elections. Critics say it will further erode democracy in the North Atlantic Treaty Organisation member state and entrench one-man rule.
Erdogan's victory paves the way for another five-year term.
An unexpectedly strong showing by the AKP's alliance partner, the nationalist MHP, may also mean Erdogan secures the parliamentary majority he seeks to govern freely.
The new system of government abolished the office of prime minister and empowers the president to take over an executive branch and form the government.
Turks were choosing both a president and new parliament Sunday in one the most fiercely fought election in years. It reached 4.587 lira to the dollar at 12:17 a.m. (2117 GMT) before easing slightly.
Recep Tayyip Erdogan is up by more than 20 points, according to a state-run agency, with 97 percent of the vote counted, although the opposition claims that most ballot boxes have yet to be opened.
But Ince said the results carried on Anadolu were not a true reflection of the official vote count by the country's electoral board.
The head of Turkey's Supreme Election Council, Sadi Guven, declared Erdogan the victor early Monday after 97.7 of votes had been counted.
"Our citizens have fulfilled their responsibility and cast their votes and have shown a very clear direction for the whole nation", Erdogan said.
Opposition parties and NGOs deployed up to half a million monitors at ballot boxes to ward against possible electoral fraud.
According to Anadolu, the CHP acquired 22.7 percent of the ballots, while its ally, IYI Party got 10.1 percent.
He also praised the high turnout in the elections.
The stakes were particularly high as the new president will be the first to enjoy enhanced powers, without even a prime minister, under a new constitution agreed in an April 2017 referendum strongly backed by Erdogan but which opponents say grants autocratic powers.
The alliance had a "parliamentary majority" in a new 600-member assembly, he said.
Erdogan has declared himself an "enemy of interest rates", raising fears he will pressure the central bank to cut borrowing costs after the election despite double-digit inflation.
He accused Mr Ince - a former teacher and MP of 16 years - of lacking the skills to lead.
Earlier on Sunday, a crowd of Mr Erdogan's supporters chanted his name as he emerged from a school after voting in Turkey's largest city Istanbul, shaking hands with people amid tight security.
But critics say he has become increasingly intolerant of dissent and opposition.