French Foreign Minister Jean-Yves Le Drian is scheduled to meet Monday with his Qatari counterpart.
Qatar's neighbors cut ties with the country over accusations that it sponsors Islamic extremism, which Qatar denies.
But Macron's score of 24 percent in the first round of the presidential race and Sunday's low turnout undermine "the illusion of Macron-mania", he said.
Her hopes of a parliamentary breakthrough appeared to have been dashed, with Kantar Public-onepoint predicting only one to four seats for the far-right party.
Ms Le Pen's party took a disappointing 13.2 per cent, well below her 21.3 per cent of the presidential first round vote.
His fledgling Republic on the Move! - contesting its first-ever election and fielding many candidates with no political experience at all - was on course to deliver him a legislative majority so crushing that Macron's rivals fretted that the 39-year-old president will be able to govern France nearly unopposed for his full five-year term.
The main victim of the vote is the Socialist Party of Macron's predecessor Francois Hollande.
If the projections from the first round are sustained, then the change that is about to happen to the National Assembly is as big as the one that occurred in 1958 when Charles de Gaulle brought in the Fifth Republic. With all first round votes counted, just over 28 percent went to Macron's party.
The conservative party The Republicans and allied centre-right Union of Democrats and Independents held 18.9%, the National Front 13.8% and the Socialists 7.45%.More news: Brooks Koepka wins US Open with 67 in final round
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She hopes to be a strong opposition force, but her party is only projected to hold about a dozen seats.
To win in the first round, the candidate must obtain an absolute majority, but no less than 25 percent of the votes of all voters registered in the constituency.
Both the Socialists and the conservative Republicans party warned voters against concentrating too much power in the hands of one party in the second round. But he looked set to capitalise with the traditional parties in disarray after troubled presidential campaigns.
Government spokesman Christophe Castaner said the 49 percent turnout - the lowest for six decades in such a vote - was "a failure of this election", acknowledging that the Macron team would need to reach out to those who stayed away.
Voter rejection of old-style, established politics - already seen in the April-May two-round presidential vote that handed power to 39-year-old Macron - was again manifest in the legislative vote.
A second round of voting will be held on Sunday in almost all constituencies between the two or three top-placed contenders.
President Macron claims his political leanings are to neither the left or the right.
To win, a candidate needs more than half of the votes cast, and they must account for at least a quarter of the registered voters - doubly challenging as the national turnout was below 50 per cent.
If the seat projections are confirmed next week, he will have a strong mandate to push through the ambitious labour, economic and social reforms he promised on the campaign trail.