HDP deputy chairman Mithat Sancar said the vote was undermined by the fact that the campaign was held under emergency rule while the party's co-leaders were under arrest, that its candidates for polling station monitors were rejected, and that state resources were used in the "yes" campaign.
Binali Yildirim made the call during an address to legislators from his ruling party, as the country's main opposition party prepared to apply to the country's highest electoral board to seek an annulation of Sunday's vote which gave President Recep Tayyip Erdogan's "yes" camp a narrow win.
"It is clear that invalidating the votes of the citizens who exercised their constitutional rights [on Sunday's referendum] will damage the voters' right to participate in the electoral process", the YSK said in a statement on its website.
Turkey's election commission on Wednesday rejected opposition applications to annul the recent constitutional referendum, broadcasters CNN Turk and NTV reported. "You can not build a change in the political system on such a controversial and unfair referendum".
President Trump plans to meet next month with Turkish President Recep Tayyip Erdogan, according to Turkish and USA officials, just weeks after Erdogan claimed victory in a referendum that vastly increased his powers and has been questioned by the opposition and global observers.
Until now, Turkey's president was required to remain above party politics, a condition which was removed in one of the referendum's 18 amendments.
Canada introduces legislation to legalize marijuana
But the bill makes good on an election promise by Prime Minister Justin Trudeau to legalize "recreational" marijuana use. Adults will be allowed to carry 30 grams in public and grow up to four marijuana plants per household.
In addition, changes to Turkey's executive branches will effectively abolish the position of prime minister, turning Erdogan's presidential role from a largely ceremonial one to an active one. Turkey's main opposition party has filed a formal request seeking Sun.
The HDP, the third largest party in parliament, filed a complaint with the electoral board on Wednesday calling for the referendum to be annulled after the CHP filed a similar appeal on Tuesday.
"The only decision that will end the legitimacy debate and ease people's concerns about the judiciary is for the High Election Board to cancel the referendum", Tezcan said. "It is completely unacceptable to call people to the streets through various communication tools and not to recognise the results", Yildirim said. There were widespread expectations he would take over the leadership nearly immediately after the vote.
Global election monitors, including from the Organization for Security and Cooperation in Europe, noted a series of irregularities, and said the decision to accept as valid ballots without official stamps undermined safeguards against fraud and was contrary to Turkish law.
Turkish Foreign Minister Mevlet Cavusoglu on Wednesday accused the OSCE of bias and deliberately putting errors into its report.
Erdogan himself has told critics to "talk to the hand", adding that Turkey will not "see, hear, nor acknowledge" political reports on the matter.