Projections show La Republique en Marche (Republic on the Move) and its MoDem ally set to win up to 445 seats in the 577-seat National Assembly.
Having an absolute majority in the National Assembly, France's lower and more powerful house of parliament, will allow Macron to govern more at ease during his five-year term.
"Working class voters vote less in parliamentary elections than in presidential ones", he said. They also blamed the long election cycle, with party primaries that started past year before the two rounds of presidential and then legislative voting, for turning voters off.
A swath of senior Socialists, including former government ministers, lost their seats in the first round.
Cambadelis called on voters to favor more political pluralism in the second round.
French President Emmanuel Macron's centrist party claimed victory in Sunday's first round of elections to the National Assembly, despite a historically low turn-out.
"France is back", Prime Minister Edouard Philippe told French TV.
The prime minister also thanked security services for protecting voting stations and ensuring a safe vote after a string of deadly extremist attacks. Polls project it could win about a dozen seats, in part because of a voting system that favors the biggest parties.
Le Pen has spent the past six years since taking charge of the FN trying to expunge the xenophobic, anti-Semitic ethos engendered by her father Jean-Marie Le Pen, who co-founded the party in 1972.
The right-wing Republican party, which only at the start of this year had seemed on course to win the Presidency under Francois Fillon, will be nearly certainly be the main opposition, with between 70 and 110 seats according to Ipsos projections.
Global desk - The centrist party of French President Emmanuel Macron looks on course to win a landslide victory following the first round of parliamentary elections. "Millions of you have confirmed your attachment to the president of the Republic's project of renewal, unification and re-conquest", Philippe declared in a statement.
She at least made it easily into the run-off in the northern town of Henin-Beaumont against 12 rivals and will fight a political novice from Macron's party, Anne Roquet.
Jean-Luc Melenchon, a far-left candidate who also scored well in the presidentials, said Macron had won a "circumstantial majority".
The Macron victory is the biggest majority seen in France since Charles de Gaulle's landslide win in 1968.
Pollsters forecast the Republicans would win 20.9 percent, the FN 13.1 percent, and the Socialists with a grouping of left-wing parties 9 percent.
Speaking to Xinhua, Madani Cheurfa, secretary general of the Center of Political Research of Sciences Po, said Macron's almost ideal performance since taking office significantly backed his camp's strong performance in the first round of the legislative election.
Less than half of voters cast their ballots, however, raising fears that the president's mandate could be weakened by a lack of participation.
There are 7,782 candidates vying for the 577 seats in the lower house of France's Parliament - so Macron's party needs 289 for a minimum majority. Top vote-getters advance to the decisive second round June 18. The FN's result showed the party is struggling to rebound from Le Pen's bruising defeat by Macron in the presidential run-off.