Projections showed Macron widening his centrist revolution, with his Republique en Marche (Republic on the Move, REM) party and its ally MoDem tipped to win between 400 and 445 seats in the 577-member National Assembly in next Sunday's second round.
"It is neither healthy nor desirable for a president who gathered only 24 per cent of the vote in the first round of the presidentials and who was elected in the second round only by the rejection of the extreme right should benefit from a monopoly of national representation", Cambadelis said.
The lower turnout was mainly attributed to two major reasons - too intensive election arrangements, and the public's doubt over the French-style democracy and its effectiveness.
Prime Minister Edouard Philippe said that despite an abstention rate estimated at just over 50 per cent, "the message of the French people is unambiguous".
French far-right leader Marine Le Pen is lamenting "catastrophic" low turnout in the first round of parliamentary elections dominated by President Emmanuel Macron's new centrist party.
"The stakes of the second round are clear", said the current mayor of Bordeaux, calling for Republicans voters to turn out in force on Sunday.
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The party's secretary general, Nicolas Bay, warned of Macron getting "a majority so big that he will have a sort of blank check for the next five years".
She also slammed the electoral system as unfavourable to smaller parties like hers.
Mr Macron's Republic on the March!
French President Emmanuel Macron's nascent political party has stormed past its traditional rivals in the first round of voting in parliamentary elections which took place Sunday.
Mounir Mahjoubi, junior minister in charge of digital affairs, said on BFM television that voters have acknowledged that the first weeks of Macron's presidency "have been exemplary" and "have allowed the French to see there is a path that suits them".
LREM, formed just a year ago to get Macron elected, fielded an unprecedented number of unknown candidates.
"We want a big majority to be able to act and transform France over the next five years", Mounir Mahjoubi, a tech entrepreneur running under Macron's Republic On The Move (LREM) banner told Reuters as he canvassed support in his northern Paris constituency ahead of the vote.
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Opinion polls showed Macrons wouldwin between 360 and 427 seats - easily a majority.
Less than half of voters cast their ballots, however, raising fears that the president's mandate could be weakened by a lack of participation.
A host of opinion polls show Macron's party taking around 30 per cent of the vote today, putting it in pole position to secure a landslide in the second round next Sunday.
Both the Republican and Socialist parties, which have traditionally governed during the time of the Fifth Republic, struggled with turnout, which was projected at 49.5% by Elabe.
The Socialist Party that held power in the last legislature looked likely so see their 314 seats reduced to as few as 20, according to pollsters' projections.
For one, many who voted for Macron in May said that they were merely voting against his opponent, the far-right extremist Marine Le Pen.
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