The left-wing New Popular Front came in second with 28 per cent while French President Emmanuel Macron's centrist bloc reached 20 per cent, the ministry said.
Exit polls had predicted National Rally (NR) winning the popular vote in a huge setback for Macron who had called the snap election after his ticket was trounced by the RN in European Parliament elections earlier in June.
The left-wing New Popular Front garnered 28 per cent of the popular vote, coming in second. (EPA PHOTO)
The result was in line with opinion surveys ahead of the election, and was met with jubilation by Le Pen's supporters.
However, they provided little clarity on whether the anti-immigrant, eurosceptic RN will be able to form a government to "cohabit" with the pro-EU Macron after next Sunday's run-off.
A longtime pariah for many in France, the RN is now closer to power than it has ever been. Le Pen has sought to clean up the image of a party known for racism and anti-Semitism, a tactic that has worked amid voter anger at Macron, the high cost of living and growing concerns over immigration.
At Le Pen's Henin-Beaumont constituency in northern France, supporters waved French flags and sung the Marseillaise.
"The French have shown their willingness to turn the page on a contemptuous and corrosive power," Le Pen told the cheering crowd.
The RN's chances of winning power next week will depend on the political dealmaking made by its rivals over the coming days. In the past, centre-right and centre-left parties have teamed up to keep the RN from power, but that dynamic, known as the "republican front", is less certain than ever.
If no candidate reaches 50 per cent in the first round, the top two contenders automatically qualify for the second round, as well as all those with 12.5 per cent of registered voters.
In the run-off, whoever wins the most votes takes the constituency.
High turnout on Sunday suggests France is heading for a record number of three-way run-offs. These generally benefit the RN much more than two-way contests, experts say.
Macron called on voters to rally behind candidates who are "clearly republican and democratic", which, based on his recent declarations, would exclude candidates from the RN and from the hard-left France Unbowed (LFI) party.
There was a high voter turnout at the first round of elections with a run-off vote still to come. (AP PHOTO)
Political leaders from the centre left and far left all called on their third-placed candidates to drop out.
"Our guideline is simple and clear: not a single more vote for the National Rally," France Unbowed leader Jean-Luc Melenchon said.
However, the centre-right Republicans party, which split ahead of the vote with a small number of its lawmakers joining the RN, gave no guidance.
Jordan Bardella, the 28-year-old RN party president, said he was ready to be prime minister - if his party wins an absolute majority. He has ruled out trying to form a minority government and neither Macron nor the NFP leftist group will form an alliance with him.
"I will be a "cohabitation" prime minister, respectful of the constitution and of the office of president of the republic, but uncompromising about the policies we will implement," he said.
The mood was gloomy at the Republique square in Paris, where a few thousand anti-RN protesters gathered at a rally of the leftist alliance on Sunday night.
Najiya Khaldi, a 33-year-old teacher, said she felt "disgust, sadness and fear" at the RN's strong results.
