Iranian President Mohammad Khatami has appealed against voter apathy after his reformist allies suffered their worst electoral defeat in six years.
The polls were seen as a test for President Khatami
The high abstention at the elections was an "alarm bell for the future" and could breed "disappointment and disenchantment with the whole system", the president said.
Returns showed a national turnout of 49%, and just 12% in the capital, Tehran.
Conservatives took 14 out of 15 council seats in Tehran alone, in a vote they said was a blow to "Western-influenced groups".
One of President Khatami's allies, Mostafa Tajzadeh, said the vote, in which reformists failed to field joint candidates, was a defeat for the whole of Iran.
"We conceded defeat because we failed to win seats in Tehran and big cities," he told a news conference on Monday.
Friday's polls mean people feel their vote in the past few years has been disrespected and is useless
"But it was a bigger defeat for the whole establishment because a large majority of people simply refused to vote."
Mr Tajzadeh, who stood unsuccessfully in Tehran, warned that disenchantment with the political system could drive people to "move beyond the system, reforms and legal opposition".
The BBC's Sadeq Saba says that although the reformists have accepted their defeat, they are also reminding their conservative rivals that there is no winner in a poll in which the majority of the people did not bother to vote.
However, our correspondent adds, the election defeat could undermine Mr Khatami's position inside the country and internationally.
Mr Khatami came to power in 1997 with a large popular mandate but correspondents say that the slow pace of reform in the Islamic Republic may be driving many of his supporters away from politics.
"Friday's polls mean people feel their vote in the past few years has been disrespected and is useless," said Mr Tajzadeh.
Tehran switches hands
Reformists took all 15 council seats in 1999
Conservatives have now taken 14
"It means people have lost hope of seeking democratic changes through the ballot."
Amin Sabooni, a columnist in the English-language Iran Daily, wrote that supporters of reform were disillusioned with their politicians:
"What the nation got was broken promises, confused priorities, internecine feuds pitting reformists against their rivals and the nonsensical conspiracy theory."
But the religious right hailed the election result as a rejection of "Western-influenced" reformists.
"The people's disaffection with them left no doubt that these Western-influenced groups, which are indifferent to the people's demands, have neared the sunset of their lives," Kayhan newspaper said in an editorial.
Test of popularity
People went to the polls on Friday to elect 905 city councils and 34,205 village councils.
Recent elections in Iran had been regarded as a test of strength between reformists and hardliners but this poll was seen as a referendum on President Khatami's popularity.
It was the second time local elections had taken place since their introduction in 1999 as part of President Khatami's concept of a civil society at the grassroots level.
Many of the estimated 41 million eligible voters were under the age of 30.