Le Pen says she will lead the opposition to Macron.
He spoke with "the French president-elect to congratulate him on his victory", White House spokesman Sean Spicer said.
If another party wins a majority, Mr Macron could be pressured to choose a prime minister from that party, a situation the French call "cohabitation".
Speaking to thousands of supporters from the Louvre Museum's courtyard, Macron said that France is facing an "immense task" to rebuild European unity, fix the economy and ensure security against extremist threats.
The President-elect will attend a party board meeting Monday afternoon.
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He has said that half of his candidates for the 577 seats in the National Assembly will be new to politics.
The transfer of power to Macron will take place Sunday, outgoing President Francois Hollande announced.
Wild celebrations broke out in many parts of Paris and across France as Macron, 39, wrapped up an overwhelming 66.06 per cent of all votes in a closely and bitterly fought battle.
Commissioning editor Tom Webber acquired United Kingdom and Commonwealth rights to The French Exception: Emmanuel Macron's extraordinary rise and risk from Kerry Glencorse at the Susanna Lea Agency.
Macron will name his prime minister next week, but could be forced to amend his choice if the legislative elections don't go to plan.
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A number of Democratic lawmakers made less direct threats, saying if what has been reported is true it is obstruction of justice . What are the grounds for impeachment? When and if he breaks the law, that is when something like that would come up.
"I will be a candidate in the presidential majority and I wish to join up to his movement, the Republic on the Move".
Michael Roth, Germany's deputy foreign minister, applauded Macron's win but said the result was marred by the fact that 11 million people in France voted for Le Pen. But in his statement, Korsia also referenced concerns over the support shown to Le Pen - a nationalist who seeks a ban on wearing Jewish and Muslim religious symbols in public, ritual slaughter and the provision of pork-free meals in school cafeterias.
More congratulations rolled in from world leaders.
"In these conditions it is especially important to overcome mutual mistrust and unite efforts to ensure worldwide stability and security".
On the financial front, European stock markets edged down in early trading as investors had been widely expecting Macron's victory.
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He was asked by Democratic President Barack Obama in 2011 to stay on for two more years and was replaced by Comey in 2013. Mueller will have sweeping powers and the authority to prosecute any crimes he uncovers.
The Stoxx Europe 600 Index slipped 0.1 per cent at the close, while the Euro Stoxx 50 Index lost less than 0.5 per cent. France's CAC 40 Index fell 0.9 per cent after rallying in the previous two sessions. Other indexes across Europe also dipped, while the euro, which briefly hit a six-month high above $1.10 overnight, was down 0.7 percent at $1.0924.
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