His AK Party took 42.5% in the parliamentary election and its nationalist allies beat expectations with 11.1%, giving their alliance a legislative majority.
"The head of the Russian state stressed that the outcome of the vote fully confirms Erdogan's great political authority, broad support of the course pursued under his leadership towards solving vital social and economic tasks facing Turkey, and enhancing the country's foreign policy positions", the statement said.
Erdogan will begin a new five-year term as president that will see changes to the Turkish constitution, which were implemented after Erdogan's faction, the Justice and Development Party (AKP), narrowly won a referendum last year.
The President used to be a largely ceremonial post until past year, when voters narrowly approved a referendum (51% to 49%) to give the President sweeping executive powers, which Erdogan has already been exercising under a state of Emergency. Erdogan's plan to take more control over interest rates are particularly worrisome for investors: The president is against raising interest rates despite stubbornly high inflation at 12% (more than twice the central bank's target).
Erdogan, accompanied by his wife Emine, waves to supporters of his ruling Justice and Development Party (AKP) in Ankara early Monday.
The secular Republican People's Party (CHP) chief Kemal Kilicdaroglu had chosen Muharrem Ince as its candidate to challenge Erdogan in the elections.
The YSK is to announce final results on Friday.
But Ince, who had faced limited airtime on television in the campaign and a near boycott by state media, said the run-up to the election had been unfair.
Tapping in to nationalist fears of outside influences in Turkey after a failed coup in 2016, Erdogan painted his political opponents as traitors to democracy.
Margot Wallstrom, Sweden's foreign minister, said Turkey's democracy has shortcomings - she cited opposition leaders sitting in jail - but said Erdogan should be given the chance to do that. Among other things, Erdogan now has the power to rule by decree, appoint Cabinet members, write Turkey's budget and appoint judges - all without parliamentary approval.
"Erdogan will feel empowered with his renewed mandate and also the absence of mandate obtained by the newly constituted opposition alliance".
Ince, 54, had condemned what he says are the excesses of the security state under Erdogan and pledged to end emergency rule if elected. "It is out of the question for us to turn back from where we've brought our country in terms of democracy and the economy", Erdogan said on Sunday night.
A report on website Nu.nl last week indicated a higher turnout among Dutch Turks but that was based on reports from the polling stations themselves.
"So far, there is little to suggest that the election will result in a new macro policy framework, which is required, in our view", the analysts said. He said his party made mistakes in the elections but declined to elaborate on them or say whether he would assume a role within it. This would have detracted from Erdogan's image of invincibility; it also would have helped the opposition to improve the morale of its supporters and to consolidate its votes in the second round, thus increasing the possibility of defeating Erdogan.