Mr Macron is now under pressure to secure support from rivals to fulfil his government’s reform agenda.
But neither Marine Le Pen’s far-right nor Jean-Luc Mélenchon’s left-green alliance are keen to work with him.
Minority governments are a rarity in France, and Mr Macron’s Ensemble alliance is 44 seats shy of a majority.
This means he will need to find support from mainstream MPs from both the left and right side of politics to help build a working majority.
Party representatives will visit the Élysée Palace separately for the high-level talks on Tuesday and Wednesday.
Analysts say the president may be eyeing a deal with the right-wing Republicans, and the party confirmed that its leader, Christian Jacob, would attend the talks.
Ms Le Pen will take part but Mr Mélenchon will not, the AFP news agency reports.
Socialist Party leader Olivier Faure and Communist Party boss Fabien Roussel, members of the Nupes left-wing alliance, will also meet Mr Macron.
France’s centrist government is desperately trying to avoid political paralysis after losing its majority, with some commentators warning of France becoming ungovernable.
Mr Macron will also have to replace three ministers who lost their seats in Sunday’s vote, and Prime Minister Elisabeth Borne’s future looks increasingly under threat.
The election on Sunday saw a low-turnout, with an abstention rate of 53%.
President Macron has laid out a series of plans to tackle the spiralling cost of living, including food vouchers and enhanced benefits. Another big reform is gradually raising the retirement age from 62 to 65, which has proved unpopular with much of the electorate.
The aim is to “build solutions to serve the French” at a time when there is no “alternative majority” to that of Macron’s ruling alliance, a presidential official, who asked not to be named, told AFP.
Opponents from the right and left aim to resist the president’s programme of reforms, although Ms Le Pen’s National Rally has said it may back measures to alleviate the cost of living crisis if their own proposals are adopted.