He warned voters against giving LREM an absolute majority next Sunday, saying it would result in "virtually no real opposition and we will have a National Assembly without any real counterbalance, without a democratic debate and not worthy of that name".
If next Sunday's vote confirms the first round, Macron will have nearly no opposition in parliament, with the traditional main parties struggling to have their voices heard.
Macron, a former Economy Minister in France's Socialist government in 2014-2016, founded the centrist progressive political movement "En Marche!"
"I am particularly concerned about the fact that 1 French person out of 2 did not vote", Valérie Pécresse, the president of the center-right Republicans party in the Ile-de-France region, told Le Monde newspaper.
Parties on the extreme right and left seemed to be faring poorly, gaining far fewer votes nationwide than they had in the first round of the presidential election, on April 23.
Melenchon, who could see his party win around 20 seats, asked French voters "not to give full powers" to the president's party in the second round next week.
At the same time, the traditional parties on the left and the right have been weakened, with the Socialists looking particularly feeble.
That would barely be above the party's score in the legislative elections five years ago and far behind its performances in regional, European and presidential ballots over the past three years.
He continued: "Next Sunday, the National Assembly will embody the new face of our republic: a strong republic, a unified republic, a republic that listens to everyone, the French Republic".
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The main victim of the vote is the Socialist Party of Macron's predecessor Francois Hollande.
Rating agency S&P Global Ratings said on Monday it was likely to raise its growth outlook for France and the euro zone now that Macron looks poised to win a huge majority. The right-wing conservative party Le Republicains ("The Republicans") won about 21% of the votes. But her National Front (FN) party was staring at yet another defeat. Le Pen, who had Europe on edge until she lost the May 7 presidential race, was trying to save herself and her party in the legislative contests. Other established political camps, left angling for what appeared would be a paltry number of seats, also had little to celebrate.
But his La France Insoumise took only 11 percent, and Kantar Public-onepoint forecast 13 to 23 seats for it and the Communist Party combined.
"France is back", Prime Minister Edouard Philippe declared triumphantly.
"Their choice has a clear meaning: they want the action taken by Emmanuel Macron, since his election to the Presidency of the Republic, to be continued", LREM Party President Catherine Barbaroux said in a statement after the exit poll results were announced.
The vote comes just over a month after 39-year-old Macron became the youngest-ever president of France, beating far-right leader Marine Le Pen by 66 percent to 34 percent in a runoff vote. His party is only 14 months old, so it held no seats in the National Assembly, whose members serve five-year terms.
Macron's movement and its smaller ally MoDem are projected to be within reach of as many as three-quarters of the 577 seats in parliament.