Nytimes.com | By PATRICK KINGSLEY

ISTANBUL — A village leader shoves four voting slips into a ballot box. An unknown arm marks three slips with a “yes” vote. An unknown hand adds five more. An election official validates a pile of voting slips — hours after they were meant to be validated.

These are four of the scenes captured in unverified videos that have helped stoke accusations of voting fraud in polling stations across Turkey during Sunday’s referendum to expand the powers of President Recep Tayyip Erdogan.
Mr. Erdogan’s “yes” campaign has claimed victory by a small margin — 51.4 percent to 48.6 — in a vote that further insulates the president from scrutiny and tightens his grip on one of the most influential countries in the region.
But while Mr. Erdogan has turned his claimed victory into a political reality, the legitimacy of his win is still in question. Opposition parties say the vote was rigged. The main opposition party formally asked Turkey’s electoral commission Tuesday afternoon to reassess the contents of multiple ballot boxes and — in a separate appeal — to annul the entire poll result. And two major international observation missions have a list of concerns over irregularities during the campaign and on the day of the vote.
One observer group said that 2.5 million votes — roughly twice the margin of victory — are under question. “It seems credible that 2.5 million were manipulated, but we are not 100 percent sure,” Andrej Hunko, a German lawmaker who observed the election on behalf of the Council of Europe, said by telephone.
Other concerns raised by the opposition and by election observers include:
■ Suspicions of ballot-box stuffing in “almost all” of Turkey’s 165,000 ballot boxes, according to the Republican People’s Party, or C.H.P., the main opposition party.
■ A decision by the electoral commission, made during the vote itself, to significantly increase the burden needed to prove allegations of ballot-box stuffing.
■ The barring of over 170 members of the opposition from participating in election observation.
■ The temporary detainment of some international election observers, preventing them from fully observing election counts.
■ Minimal “no” votes in an opposition stronghold in southern Turkey.
■ At least one allegation of “no” votes being removed from ballot boxes and deposited in a building site in the same area of southern Turkey.
■ The unfairness of the campaign itself, which observers from the Organization for Security and Cooperation in Europe described as taking place on “an unlevel playing field.”
Turkey’s electoral commission has delayed announcing an official result, and it said it would assess allegations of fraud.
Appeals concerning individual ballot boxes are first assessed at a local level, then at a regional level and fina
lly by a national board. The C.H.P.’s appeal to annul the entire process will be assessed directly by the national board. Both processes, according to the commission head, are likely to be completed with 12 days.
But there are few precedents for the annulment of electoral results in Turkey, a trend most analysts do not expect to be suddenly bucked this week.
Sunday’s result seemed particularly unlikely to be overturned after the head of the electoral commission defended the legitimacy of the referendum in a speech.
In the process, the commission has opened itself up to allegations of bias. “You are not a referee, you are taking sides,” Osman Baydemir, a lawmaker and spokesman for the third-largest party in Parliament, the Peoples’ Democratic Party, or H.D.P., said in a speech.
The opposition is particularly concerned about the commission’s decision, after voting began on Sunday, to allow unvalidated ballots to be counted unless it could be proven that they were inserted into the ballot box specifically to tamper with the results.
Turkish electoral law stipulates that ballots should be stamped by election officials and then placed in a stamped envelope before the envelope is placed in a ballot box. Unstamped papers, or papers within unstamped envelopes, are invalid by law.
On Sunday, the commission decided otherwise, saying that similar rulings had been made in multiple elections in the past. But some legal experts said the decision had no precedent, and in fact contradicts a ruling made by the same commission in 2014. The O.S.C.E. also said the decision “undermined an important safeguard and contradicted the law that explicitly states that such ballots should be considered invalid.”
Kerem Gulay, an expert on Turkish electoral law at the University of Amsterdam law school, said, “Changing the rules of the game after the voting started and half an hour before voting in the eastern provinces stopped — I haven’t heard of anything like that in recent electoral history worldwide.”
Specific allegations of ballot-box stuffing emerged in the southern province of Sanliurfa. In one district, “no” voters formed less than 1 percent of the total, even though the H.D.P. won over half the votes in the area at the last parliamentary elections, in November 2015.
Unverified photographs later emerged that seemed to show bags of “no” votes abandoned in a building site in the province. In another part of the same region, an H.D.P. lawmaker said he had witnessed multiple violations, including the stuffing of 400 ballots into a box that was only meant for 360 voters.
“Unconcealed voting, people voting multiple times, or on behalf of other people — these were widely practiced in rural Urfa,” said the lawmaker, Ibrahim Ayhan, using an informal name for the region. “And the law enforcement officers did not intervene as they should have.”
More generally, international election observers said on Monday that the poll had not been conducted in a fair environment.
The 24-person team from the O.S.C.E. highlighted how the poll was held amid a state of emergency that had involved tens of thousands of people being arrested, including lawmakers from the H.D.P., and over 1,500 civil society organizations being shuttered. “No” campaigners faced physical intimidation and limitations on their ability to hold rallies and access public media, the group said.
A separate mission from the Council of Europe had similar findings. Mr. Hunko, the German lawmaker, said he had been detained by the police in southeastern Turkey, preventing him from properly observing the counting process.
“We were hindered by police forces in a way that I have never experienced in any observation mission,” said Mr. Hunko, who said he had participated in at least 15 such missions across the world.
Mr. Hunko said the situation was particularly concerning in the southeast, where the displacement of hundreds of thousands of Kurds may have left many without a fixed address, and therefore without the right to vote. The arrest of tens of thousands of people, particularly in the Kurdish region, also cast doubt on whether the vote was free.
“Yesterday was not a free or a fair election,” Mr. Hunko added. “It was not fair generally and it was not free in part of the country, the southeast. If you have thousands in prison and they cannot vote, you cannot talk about free elections.”
Hundreds of demonstrators have gathered in each of Turkey’s three largest cities since Sunday night to protest the alleged violations.
Mr. Erdogan, however, rejected their concerns and those of other countries, which he described as “politically motivated.” The referendum was the “most democratic election” of any Western country, he told supporters at a rally.
“Know your place,” Mr. Erdogan said in a barb directed at foreign observers.

Follow Patrick Kingsley on Twitter @PatrickKingsley.