Aminata Touré, head of the presidential coalition said her side won 30 of the 46 departments in the West African country and overseas constituencies.
"This undoubtedly gives us a majority in the National Assembly," Toure told reporters late Sunday.
"This undoubtedly gives us a majority in the National Assembly," Aminata Toure told reporters late Sunday."
Toure however acknowledged her coalition had been defeated in the capital, Dakar.
But on Monday the main opposition coalition expressed "astonishment" at Toure's remarks, claiming it had won a "comfortable majority" and that the presidential camp was "looking to once again confiscate the vote".
It also failed to specify the number of seats or what kind of majority it was claiming.
"We call on national and international opinion to act as witnesses against any attempt to manipulate the results," the opposition said in a statement.
The opposition had hoped the elections would impose a cohabitation, or divided government, on Sall and curb any ambitions he may have for a third term.
Opposition coalition Wallu Senegal ("Save Senegal" in Wolof) said Sall had failed to obtain a majority and that prominent politicians including former prime minister Toure had been beaten.
This year, eight coalitions are in the running, including Yewwi Askan Wi ("Liberate the People" in Wolof), the main opposition coalition headed by former presidential candidate Ousmane Sonko, who came third in the 2019 presidential election.
Ahead of the poll, Yewwi Askan Wi joined forces with Wallu Senegal, led by former president Abdoulaye Wade.
The two groups agreed to work together to obtain a parliamentary majority and "force governmental cohabitation".
The vote took place against a backdrop of rising prices, partly because of the Ukraine war.
The opposition has questioned the priorities of the government, which has highlighted its subsidies for oil products and food as well as infrastructure building.
The 21-day election campaign passed in a mostly calm atmosphere.
The pre-campaign period, however, was marked by violent demonstrations that left at least three people dead after several members of the main opposition coalition, including Sonko, were banned from taking part.
Sall, 60, was elected in 2012 for seven years then re-elected in 2019 for another five. He has been accused of wanting to break the two-term limit and run again in 2024.
He has remained vague on the subject, but any defeat of his supporters in Sunday's vote could upset such plans.