Hurriyet said around 14 protesters were detained by the police in the Mediterranean province of Antalya, where a majority of people voted against the constitutional changes in Sunday's referendum.
Opposition parties have argued that the constitutional amendments do not provide for any checks and balances on Erdoğan's power, setting the stage for one-man rule in Turkey.
A GOP chairman said Tuesday he is troubled by Turkey's "creeping authoritarianism" after President Recep Tayyip Erdoğan declared victory this week in expanding his powers.
"Saying the referendum fell below global standards is unacceptable", the ministry said in a statement, adding that previous "politically charged" comments from OSCE monitors showed the team arrived in Turkey with prejudice and disregarded principles of objectivity and impartiality.
The queues formed as the main opposition party was scheduled to formally request that the electoral authority annul the referendum over the ballots lacking the official stamp.
"There is only one decision to ease the situation in the context of the law - the Supreme Election Board (YSK) should annul the vote", the Dogan news agency quoted CHP deputy leader Bulent Tezcan as saying.
Thousands of people took to the streets of Istanbul to protest the results of the referendum that extended powers of Turkish President Recep Tayyip Erdogan.More news: Red Bull loses speed when it matters in F1 Bahrain qualifying
"The motion which will be submitted to parliament on the extension of state of emergency for three months as of April 19, 2017 at 1.00 a.m. [2200GMT Tuesday] was signed by the Council of Ministers", said Kurtulmus.
Mr Yildirim said the "the path to seek rights" should be limited to legal objections and urged the opposition to accept the vote's outcome.
Monitors from the Organization for Security and Cooperation in Europe, who also listed numerous irregularities, said the board's move undermined important election safeguards.
The German government has also questioned the vote after the European Union called for a probe into the result.
US President Donald Trump phoned Erdogan to congratulate him on the referendum win with no mention of voting irregularities or human rights concerns.
A government spokesperson said: "We will follow closely how Turkey behaves on this".
In an interview with the German daily Bild on Tuesday, Foreign Minister Sigmar Gabriel underlined Turkey's strategic importance for Germany and the EU, adding that he favored a continuation of an EU-Turkey dialogue despite recent tensions.