Russia's opposition movement recorded its most telling electoral result in 13 years of Vladimir Putin's rule on Sunday when candidates for mayor in two of the country's largest cities pulled off impressive results against incumbents.

Opposition leader and anti-corruption activist Alexei Navalny won 27.24% of the vote for the Moscow mayoralty, but he immediately disputed the result, saying it was marred by "many serious violations".

He said in a statement: "We consider the official election results to be deliberately falsified."

Official results on Monday morning gave Kremlin ally Sergei Sobyanin, the acting mayor, 51.37%, enough to clear the 50% threshold needed to avoid a second-round runoff.

The Alliance of Observers, however, counted 49.7% for Sobyanin and 28.3% for Navalny.

Navalny's result – achieved with none of the financial, administrative and media advantages that incumbents enjoy – was interpreted as a clear sign of disaffection with the ruling elite.

In Russia's "third capital" of Yekaterinburg, anti-drug activist Yevgeny Roizman appeared to have beaten his opponent from the ruling United Russia party in the mayoral race.

The head of the Yekaterinburg electoral commission said on Monday morning Roizman had won by a margin of more than 3%, but that this result was still being finalised. Several exit polls on Sunday showed Roizman had won by a slim margin. Such a result would also be an embarrassment for the Kremlin.

In the lead-up to the Moscow election, many experts had said 20% would be an impressive result for Navalny, whose rating was in single figures when the early mayoral vote was called in June.

The opposition leader's unexpectedly high result, which he attained after tenacious street campaigning, appeared to mark an important turning point in Russian politics. For the most part, previous elections have been dominated by candidates from parties loyal to the Kremlin.

"The old political system is dead," said liberal political figure Leonid Gozman on the opposition-leaning TV channel Dozhd. "What happened in Moscow and Yekaterinburg … is related to people who are not associated with any party" in the Kremlin-controlled political system.

As the vote counting dragged on, both cities appeared poised for a tense couple of days. One picture circulating on Twitter showed riot police deployed outside the seat of the Yekaterinburg government.

The Moscow Electoral Commission had promised a final result by midnight thanks to newly installed electronic voting machines, but late on Sunday night delayed the announcement of the final result until 10am on Monday.

Speaking to journalists, Navalny said the delays in announcing official results were an indication of the "clear falsification" of votes. He said Sobyanin's results remained above 50% only due to ballot-stuffing outside polling stations, such as when counting votes cast from home. "We demand a second round. We ask Muscovites to come out to the streets if Sobyanin violates their right to vote," he said.

On Sunday afternoon, the Navalny campaign was already planning a protest rally for Monday night.

In July, Navalny was given a five-year prison sentence for extortion in a highly politicised trial. If his appeal against the verdict is unsuccessful, he will be ineligible to hold office in Russia.

Opposition candidate and former MP Gennady Gudkov fared less well in the Moscow region gubernatorial race, where the United Russia candidate Andrei Vorobyov reportedly won with over 70% of the vote.

Election observers in Moscow reported numerous minor violations. In the runup to the election, analysts predicted that falsifying votes cast from home (citizens can request electoral workers to make home visits) would be the most likely method of cheating, but the percentage of such votes was reportedly small.

Yelena Maliyeva, an electoral observer who said she supported Navalny, said she had discovered no irregularities at her polling station in south-central Moscow. However, she said she was prepared to stay all night to prevent violations, as she did during last year's presidential vote.

"In the presidential election, all the dishonest stuff happened after the polling place was closed. Then there were attempts to falsify votes," she said.

Voter turnout was, as expected, low across the country (besides the Moscow mayoral election, seven gubernatorial elections and 16 regional legislative elections were held on Sunday). In Moscow, it was reportedly under 30%.

Many saw the Moscow vote as a referendum on competitive elections. Alexander Lebedev, the Russian banker who owns the Independent and the Evening Standard, tweeted that he would vote for the first time in years: "I'm headed to the polling station. I have to, there's an actual choice."

Even Maria, an election observer and Sobyanin supporter who declined to give her last name, admitted that Navalny had made the election interesting. "That's his one plus," she said.

Sobyanin had ordered ruling party municipal deputies to give Navalny the signatures necessary to enter the race in what many saw as an attempt to lend his victory legitimacy and improve his political status. But the strong result for the opposition candidate calls into question Sobyanin's political rise, which some had speculated could go as far as the prime minister's chair.

Several officials, including Sobyanin's campaign manager, praised the fairness and competitiveness of the elections in an apparent shift in rhetoric. "Do I understand correctly that the official statement about the 'most fair elections' is an admission that the rest were 'not the most fair'?" tweeted socialite and television host Ksenia Sobchak.

Speaking at a United Russia meeting, prime minister Dmitry Medvedev said United Russia's victory in the majority of regional elections showed it "is able to work under in conditions of competitive elections."