With the government set to be announced on Tuesday - but postponed to Wednesday - new Prime Minister Edouard Philippe defended his decision to accept the appointment.
"I said to myself that the situation we were in was sufficiently unique for us to try something that has never been tried," he told TF1 television.
As well as members of Macron's Republic on the Move! party, ministers are expected to come from the ranks of the mainstream left Socialists and, like Philippe, the mainstream right Republicans.
The new PM, an ally of former prime minister Alain Juppé who failed to win the Republicans presidential nomination, has "put himself outside our family", Republicans secretary general Bernard Accoyer said after the appointment.
The party's executive would discuss what to do about Philippe's case and those of any members who join the new government, Accoyer said.
But he insisted that "the right is holding up", despite the upheaval caused by presidential candidate François Fillon's failure to reach the second round of the presidential election and Macron's "masterstroke" in naming Philippe, which means that "a certain number of our friends ... may allow themselves to be tempted by the appeal of power".
"All this does not seem healthy for democracy to us," Accoyer commented.
Phoning potential defectors
Macron's recruitment of ministers from other parties than his own was not "political restructuring" but "dynamiting", François Baroin, the MP who is in charge of the Republicans' parliamentary election campaign, said.
The party is to fight the election on a programme of tax cuts and it has "deep disagreements" with Macron's programme on the matter, he said.
Philippe, whose government will last the four weeks to the general election, will have to "support candidates he doesn't know ... and defend a programme he has fought against", Baroin commented.
But the party's liberal wing, headed by Juppé and former agriculture minister Bruno Le Maire, have been fighting its lurch to the right for some time and several of its members could be tempted by Macron's "neither right not left" stance.
Baroin and Accoyer have been telephoning Republicans they fear might defect to dissuade them, according to Le Monde newspaper, which said that many of Le Maire's colleagues did not believe his assurances that he would not join the government.
And MPs who do not quit the party before the parliamentary poll may want to work with a Macron government after it, threatening a further split in the ranks.
On Monday 25 signed a statement calling on their party to "respond to the hand held out by the president".
Macron's tactics - "trying to destabilise [the other parties] by opening my arms to them", as he put it in a recent TV documentary - have already deepened the crisis in the Socialist Party and Defence Minister Jean-Yves Le Drian was expected to be invited to stay in his job in the new government.
The new president's actions so far have at least pleased the bosses' union Medef.
"For the moment we are on a cloud," its leader, Pierre Gattaz, told Cnews TV on Tuesday. "For the moment Macron is faultless."
Gattaz urged the new government to "act fast" on further changes to labour law, calling for "flexisecurity" in the jobs market, capping of compensation for unfair dismissal and priority of company-level agreements over industry-wide ones.
Complaints that the president plans to change the law by decree are "surrealist", the boss of bosses commented, arguing that the method does not preclude consultation.
The leader of the one major union to accept the outgoing government's changes to labour law warned against forcing new measures through, however.
"With society in a state of anxiety the head of state must be vigilant when it comes to method," CFDT chief Laurent Berger warned.
Macron has said he will reform labour law over the summer and Prime Minister Philippe said Tuesday that he would be getting down to work on the question straight away.