The Republican People's Party (CHP) has questioned the legitimacy of the close result, citing irregularities in the electoral process.
President Recep Tayyip Erdogan's push for an executive presidency succeeded with just over 51% of the vote.
The win was met with both celebrations and protests across Turkey.
The CHP is refusing to accept the Yes victory and is demanding a recount of 60% of the votes, criticising a decision to pass unstamped ballot papers as valid unless proven otherwise.
