Nasser Jawdeh, a government spokesman, said on Wednesday that the four members of the Islamic Action Front (IAF), including a woman, were free to take up their posts but added "the decision is theirs".
Nader Zuheirat, Jordan's municipalities minister, described the voting process as "successful".
But IAF secretary general Zaki Bani Rsheid dismissed the results and said the party would ask its winners to resign.
'Funeral of democracy'
"These results are of no concern to us. We pulled out all our candidates yesterday [Tuesday] from the race and the results will not change anything," he told AFP, describing the elections as "a funeral of democracy".
The IAF is the political arm of the Muslim Brotherhood movement and has 17 seats in the 110-member parliament.
Earlier, Bani Rsheid said the party was considering whether or not to field candidates in legislative elections due later this year.
"We might boycott dealing with the municipalities or even boycott the upcoming elections. All options are open," he said.
The opposition party withdrew its 25 candidates from the municipal race on Tuesday, accusing the government of fraud, a "democratic massacre" and "treason".
The IAF accused the authorities of manipulating votes cast by military personnel who were taking part in municipal elections for the first time.
Maaruf Bakhit, the prime minister, said the opposition pullout was "illegal" as any withdrawal had to come a day before the election.
Jawdeh echoed him at Wednesday's news conference and warned that the government considered any criticism of the armed forces as a "red line".
According to final results given by Zuheirat more than 1.1 million Jordanians out of 1.9 million who had registered cast their ballots to elect 965 council members and mayors from 2,686 candidates in 94 municipalities.
The vote was the first since a law was passed earlier this year granting women a 20 per cent quota - or 218 council seats - and reducing the voting age from 19 to 18 to expand the electoral base.
Zuheirat said that 20 women won council seats outside the quota and that only one woman out of six had won a race to be mayor.
Polling was extended into Wednesday in Amman because turnout on the previous day was less than the required 50.1 per cent in some districts.