The provisional results put the party ahead of the Justice and Development party (PJD), which has roots in political Islam, with 47 seats.
The PJD had expected to fare much better and on Saturday the party's leaders accused unnamed opponents of "using money" to win.
"We will respect the commitments that we have signed with our friends ... we must work towards a common position on the formation of a government," said Abbas El Fassi, secretary general of Istiqlal, vowing to keep an alliance with the socialists.
The Reuters news agency reported Saad Eddine Othmani, leader of the PJD, as saying: "Many candidates used money. We found ourselves in the election campaign facing money instead of political parties."
A series of special reports
He said he thought the PJD was "the [real] winner of the elections".
Chakib Benmoussa, Morocco's interior minister who had announced the preliminary results, said the government would examine any evidence of vote-buying in the parliamentary polls.
"We took every measure to prevent such flaws and shield the election process from any illegal influence. We are ready to look at any complaint backed by evidence," he said.
Foreign observers, though, said the elections were orderly and professional but marked by "isolated irregularities".
"There are no chances of Islamic groups winning as most people in Morocco are enjoying its liberal culture"
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A statement from a team deployed by the US-based National Democratic Institute for International Affairs said: "Generally speaking the vote took place in an orderly fashion, even if members of the delegation were witness to or were informed of isolated irregularities on election day."
Meanwhile, the International Observer delegation to the elections said the polls were characterised by a spirit of transparency and professionalism despite reports of isolated irregularities.
In a press conference held at Hilton hotel in Rabat on Saturday, the delegation urged the Moroccan government to undertake further political reforms in order to encourage widespread engagement in the political process.
"The low voter turnout and significant number of protest votes suggest that Moroccan authorities will need to undertake further political reforms," the delegation said in a preliminary statement.
Record low turnout
The delegation also noted that despite substantial progress in promoting women’s participation in parliament, the 2007 elections did not appear to have furthered women’s political participation.
Preliminary results say only 34 women have won in the current elections.
Provisional figures showed a record low turnout of 37 per cent for the elections, Morocco's first elections to be monitored by foreign observers.
Average voter turnout in rural areas was 43 per cent and in urban areas, it was 34 per cent.
At 27 per cent, the turnout was lowest in Casablanca, one of Morocco's main cities, officials said.
Reda Lamrini, a political analyst in Rabat, told Al Jazeera that regardless of the turnout, the elections represented "year zero for democracy in Morocco".
Observers said the Islamists had not grasped the need to pick strong local candidates.
Mohamed Darif, a political analyst, said parties like Istiqlal are "electoral machines that know how to win over their clientele".
"In a conservative society like Morroco, people don't vote for groups but for people according to their religion, ethnic background and then their political programme."
Among the other parties, provisional figures showed the Popular Movement (MP) and the National Rally of Independents (RNI) with 43 and 38 seats respectively.
The Socialist Union of Popular Forces (USFP), the dominant party in the ruling coalition which has Istiqlal as its junior partner, won 36.
Parties from the ruling coalition together won 102 seats.
Final official figures will be released on Sunday evening.
A complex voting system makes it almost impossible for any group to win an outright majority, and whatever the outcome, the Istiqlal is likely to need partners from other parties, possibly including the PJD.
Real power, though, will remain with the king, who is executive head of state, military chief and religious leader.