"Calling people to the street is wrong and is outside the line of legitimacy", Mr Yildirim said, adding that "we expect the main opposition party's leader to act more responsibly".
But Bulent Tezcan, deputy chairman of the CHP, told reporters Monday that the party would appeal to the European Court of Human Rights if the electoral body didn't void Sunday's referendum result.
In Ankara, Fatma Korur, 46, said she was exercising her constitutional right to object to "illegal" results.
Voting was already underway on Sunday when the electoral authority announced it would start accepting unstamped ballots - a decision that the opposition said should invalidate the results.
Opposition parties are filing their objections to the electoral board Tuesday for the decision to count as valid ballots that did not bear an official stamp and other alleged irregularities.
On Monday, global election monitors delivered a scathing verdict on the conduct of the referendum.
Two worldwide observer missions said the referendum campaign had been conducted in an unfair environment in which opposition voices were suppressed.
"You can not come to Turkey and interfere in its politics", Cavusoglu said, calling the observer missions' findings "biased".
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The petition of the CHP cited a number of irregularities during both the voting and counting processes for the referendum, specifically underlining that the YSK's decision to count unsealed ballot papers as valid increased suspicions of fraud.
The referendum results cement a yearslong effort by Erdogan - who has served as President since 2014, following almost a decade as Prime Minister - to consolidate his position.
A defiant Erdogan has dismissed the complaints, saying the vote had finally put an end to debate over the powerful presidency he has long sought. Anti-Erdogan campaigners faced physical intimidation and restrictions on their ability to hold rallies and to appear in the news media.
"Look, the Middle East is a pretty rough neighborhood, and sometimes you have to get together to help them beat the bullies, like Syria", Sanders said.
Dieter Kempf, president of the BDI lobby group, says the result of the vote "is worrying" and suggests Turkey is moving further away from European values.
Though tens of thousands of people have been detained for political reasons in Turkey in recent months, these are the first political arrests reported since the referendum. Most of the changes come into effect after the next elections, scheduled for 2019, even though holding early elections would not be out of the question.
Turkey's prime minister has called on the opposition to respect the result of a referendum that will expand the powers of the office of the president.