The move appears to have paid off as Macron's party, which has grown out of his grass-roots movement, is projected to record a stunning victory.
The result would give Macron one of the largest parliamentary majorities since the end of the Second World War.
There was more good news for Macron as five of his six Cabinet ministers running in the elections are leading in their respective races and have good chances to win in next Sunday's run-off.
The meeting between May and Macron follows the latter's political party, En Marche, claiming victory in the French parliamentary elections.
If no candidate manages to achieve that target, then all candidates who won at least 12.5% of registered voters go to the second round, where the victor will advance to Parliament.
"The huge abstention rate shows that there is no majority in this country in favour of destroying the labor code, nor for reducing liberties, nor for ecological irresponsibility, nor to pander to the rich - all things that figure in the president's program".
Conceding that the party was facing "unprecedented" losses, Cambadelis appealed to voters to rally behind Macron's rivals to avoid the president monopolising power.
The En Marche! party was predicted to secure up to 425 of the 577 seats as the first voting round got under way yesterday.
Two parties, Le Pen's National Front and the small centrist MoDem party, an REM ally, are meanwhile under investigation over alleged expenses fraud at the European Parliament.
"It is neither healthy nor desirable for a president who gathered only 24 percent of the vote in the first round...and who was elected in the second round only by the rejection of the extreme right should benefit from a monopoly of national representation", Socialist party leader Jean-Christophe Cambadelis said.
Polls suggest the elections will strongly favor Macron's party and dramatically shake up French politics, punishing the traditional left and right parties and leaving no single strong opposition force.
The Socialists, the party of former President Francois Hollande, won just 7.4 per cent.
If the projections of 400 to 440 seats for Macron's camp are confirmed, Macron will have a strong mandate to implement his campaign promises of boosting economy and reducing deficit. The FN's result showed the party is struggling to rebound from Le Pen's bruising defeat by Macron in the presidential run-off.
The FN leader is now a lawmaker in the European Parliament but is hoping to win a legislative seat in France for the first time.
Turnout was markedly down on Sunday compared with the last parliamentary election, reflecting a degree of fatalism among Macron's opponents in the face of his advance as well as a degree of election fatigue, experts said.
German Chancellor Angela Merkel congratulated the French President on Monday.
"I've voted seven times in the last few months", voter Jean-Luc Vialla said after casting his ballot in an eerily quiet voting station in Paris where voters came in a trickle.
The weak turnout will likely narrow the second-round field, because candidates need the support of 12.5 per cent of registered voters to qualify.
German Chancellor Angela Merkel congratulated Mr Macron on the "great success" of his party.