With 46 percent of votes counted from Sunday's balloting, the Interior Ministry said Macron's Republic on the Move party had more than 26 percent of votes in the elections for the 577 seats in the National Assembly.
It would likely dramatically shake up France's political landscape.
As when voters turned the previously unelected Macron into France's youngest president last month, Sunday's first round of voting in two-stage legislative elections again brought stinging black eyes to traditional parties that, having monopolized power for decades, are being utterly routed by Macron's political revolution.More news: Parliamentary elections: Emmanuel Macron's party charging towards landslide victory
French far-right presidential candidate, Marine Le Pen, right, poses for a selfie with a supporter after the first round of parliamentary elections in Henin Beaumont, Northern France, Sunday, June 11, 2017.
Pollsters said well over 30 per cent of voters had picked Macron's party in the first round, a result that they said could deliver him as many as three-quarters of the seats in the lower house after next week's second round.
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.
"We had a recent (presidential) election which shook up the classic parties and I think that the legislative elections give Macron the possibility to show what he is able to do".
The results, if confirmed, are another blow to the country's mainstream Socialist and conservative parties already reeling from Macron's election in May, which blew apart the left-right divide that has shaped French politics for the past century.
"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.More news: Brooks Koepka caps a record week with US Open title
"For the past month, the President has shown confidence, willingness and daring in France and on the global stage", Mr. Philippe said, calling the result a vindication of Mr. Macron's "winning strategy".
Morning turnout was lower on Sunday than it had been five years earlier, when parliamentary elections were last held.
The FN's result showed the party struggling to rebound from Le Pen's bruising defeat by Macron in May's presidential run-off.
Pollsters projected her party, which is still reeling from her disappointing showing in the presidential run-off vote against Macron, will next week win just a small handful of seats - perhaps as few as one.
But the weaker turnout, if borne out in the afternoon, would narrow the second-round field, because candidates need the support of 12.5 percent of registered voters to qualify.More news: UK government scrambles to limit fallout from London fire
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