Major results of all available exit polls showed that LERM won up to 33.5 percent of votes, ahead of the conservatives which collected between 20.8 percent and 22 percent.
Eying to form a strong opposition, the far-right National Front collected up to 14 percent while the outgoing ruling Socialist Party reported a poor score of between 9 and 10 percent.
Following the first result of parliamentary competition's first leg, LREM and its allies were likely to win between 415 and 455 seats out of the 577-seat lower house of parliament, securing a landslide majority.
The Kantar Sofres-onepoint estimate, made for French newspaper Le Figaro, put the number at between 400 and 440 seats for LERM.
"With this result, there is a desire of the French to be coherent and want to give a majority to the President of the Republic, Emmanuel Macron," government spokesman Christophe Castaner told TF1 news channel.
In his first political test at home, Macon, who created LREM only one a year ago, named 428 candidates, including 214 female faces, with half of them are from civil society and had never held an elected post.
By 5 pm local time (1500 GMT), 40.75 percent had cast their ballots, the lowest turnout in the 5th Republic, compared with the same time of day in the first round of 2012, when the figure stood at 48.3 percent.
Opinion pollsters predict Sunday's turnout to hit record low of 49 percent, mirroring the French people's growing disinterest in legislative election.
A second and final round of voting is scheduled for June 18 to determine the makeup of an assembly that Macron, at the start of a five-year term, needs to implement his campaign promises of boosting economy and reducing deficit.
Under France's electoral rules, only candidates who win more than 50 percent of votes in the first round win the seat outright. If there is no clear winner, all candidates who win more than 12.5 percent in the first round qualify for the second round next Sunday.
