"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".
President Emmanuel Macron's new party is set for a landslide victory in the latest round of the French election, allowing him to govern the country nearly unopposed for the next five years.
There is some good news for Le Pen though, with the FN leader on course to win Hénin-Beaumont and finally take her seat in the Assembly.
Pollsters said well over 30 percent of those who voted had picked Macron's party in the first round, a result which they said could deliver him as much as three quarters of lower house seats when the second round results come in next week.
La Republique en Marche (The Republic on the Move, LREM) and allies, with an estimated 32.9 per cent of the vote, is expected to take between 400 and 440 of the assembly's 577 seats in next week's second round, according to a Kantar Public-onepoint forecast based on partial results.
Mounir Mahjoubi, junior minister in charge of digital affairs, said on BFM television that voters have acknowledged that the first weeks of Mr Macron's presidency "have been exemplary" and "have allowed the French to see there is a path that suits them".
They include tech entrepreneur Bruno Bonnell, who campaigned by sticking photos of him and Mr Macron on the side of a rented van in Villeurbanne, eastern France.
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Like other senior politicians from established parties not connected with Macron's meteoric rise to power, Baroin also bemoaned the low turnout, which at around 49% was the lowest first round showing since the Fifth Republic was born in 1958. Interior Ministry data showed 40.75 per cent of registered voters had cast ballots by mid-afternoon, well below the 48.31 per cent at the same time in the 2012 election.
Voters said polls that had predicted a large majority for Macron's camp likely dissuaded people from turning out.
Macron has enjoyed a smooth start in the five weeks since he beat far-right candidate Marine Le Pen to become France's youngest president, naming a Cabinet that crosses left-right lines and making a big impression at global summits.
"Working class voters vote less in parliamentary elections than in presidential ones", he said. French citizens were electing 577 lawmakers to the country's National Assembly, the lower house of parliament, out of more than 7,800 candidates.
The conservative Republicans had 16 per cent, the far-right National Front 14 per cent, the far-left party of Jean-Luc Melenchon had 10 per cent and the Socialists - who dominated the outgoing National Assembly - with just seven per cent.
FN vice-president Florian Philippot admitted to "disappointment" and called on voters to "mobilise massively" for the June 18 second round.
She hopes to be a strong opposition force, but her party is only projected to hold about a dozen seats. Its chief, Jean-Christophe Cambadelis, confirmed he had been eliminated from his long-held Paris seat, a symbol of his party's stunning demise after five years in power.