Prime Minister and AKP leader Binali Yildirim said Erdogan can rejoin the party he founded in 2001 once official results of the plebiscite, granting him sweeping powers, are announced.
The minister added: "In the meantime, coherent with Turkey's membership in the Council of Europe, we are hoping for a cooling of internal tensions in the country, and, in addition, involvement of the opposition in the implementation path of the reforms".
Government figures say some 75 percent of Turkish Belgians backed President Recep Tayyip Erdogan's acquiring more powers.
Unlike U.S. President Donald Trump, the European Union would not congratulate Erdogan on his triumph, a Western official with knowledge of EU policy told Reuters.
The Turkish referendum is due to eliminate the prime minister's office and give the country's president sweeping powers and almost complete control of the government - authority not originally granted under the country's constitution.
Mr Erdogan yesterday hailed the vote as a major and much-needed step in restoring stability, saying it was the first time that Turkey had changed its political system through "civil politics".
Around 1,500 people protested the outcome of Turkey's referendum in central Istanbul late Wednesday, the fourth night since the vote on expanding President Recep Tayyip Erdogan's powers.
"Such a speculative statement from a spokesperson can not be accepted", Turkey's EU Affairs Minister Omer Celik told reporters at a televised press conference, calling on the EU to "respect democratic processes".
The Kremlin said that Putin phoned Erdogan and congratulated him on the "successful conduct" the referendum.
Representatives from a coalition of global bodies said the vote took place on an "unlevel playing field", with the "yes" campaign dominating media coverage. This would allow Erdogan to rejoin the governing AK Party he co-founded, or to lead it.
On Monday, worldwide election monitors delivered a scathing verdict on the conduct of the referendum.
"Where dictatorships exist, you don't have to have a presidential system".
The European Union also urged a probe into the poll fraud claims after global observers voiced concerns, but US President Donald Trump called his Turkish counterpart to offer his congratulations.