A Macron aide denied that any eventual revision of the wealth tax would represent a major climb-down by Macron, a pro-business former investment banker, adding that the president remained committed to his reform drive.
French protesters are welcoming Macron's decision to scrap a fuel tax rise - but say it may not be enough to contain public anger.
Turnout for the protests had fallen from about 280,000 three weeks ago to 136,000 last Saturday, with some of the violence, vehicle burning, spray painting and damage to Paris' historic monuments alienating supporters.
Philippe pointed out that the tax issue shouldn't put "the nation's unity in danger", also announcing that the national debate on how to tackle climate change without burdening the wallets of French citizens will begin in mid-December.
On Tuesday, Philippe announced a freeze in electricity and natural gas prices until May 2019, and warned protesters against more disruptions.
Seven people died and hundreds were severely injured.
Demonstrations against what would have been one of Emmanuel Macron's flagship policies began on 17 November.
The "yellow vests" are largely made up of modest earners from rural and small-town France, and many want Macron's proposed tax cut for the richest repealed.
Two groups blockading petrol depots in Brittany said they would stand down following the announcement of the measures, which will cost public coffers some two billion euros ($2.3 billion).
Numerous demonstrations were over a new university application system. "If at the end of these discussions no good solutions have been found, we will accept the consequences" Mr Griveaux said.
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The French government proposed to tax carbon, which would have added about 15 cents a gallon to the price of gasoline, or a little less than 3 percent, starting January 1.
U.S. President Donald Trump appeared to mock Macron over the policy shift, which could make it harder for France to meet its Carbon dioxide emissions reduction target, a core element of the Paris climate agreement of 2015.
"I am glad that my friend @EmmanuelMacron and the protesters in Paris have agreed with the conclusion I reached two years ago", Trump tweeted.
"The Paris Agreement is fatally flawed because it raises the price of energy for responsible countries while whitewashing some of the worst polluters".
"Trump also retweeted a false claim from American conservative student activist Charlie Kirk that said: "'We want Trump' being chanted through the streets of Paris".
Experts say the government may have reacted too late to the street protests - a regular feature of French political life which have repeatedly forced previous presidents into U-turns.
Protests last Saturday caused heavy property damage in Paris and other French cities. The yellow vest protesters have called him "president of the rich".
"The Yellow Vests wish to act on Saturday", he replied.
Macron had asked political leaders to meet the protest organizers this week. On Tuesday night, he was jeered as he travelled to a regional government headquarters that was torched by protesters over the weekend.
Negotiating with the protesters, named for wearing high-visibility yellow vests "gilets jaunes" has been hard for the government as the leaderless activists are spread throughout rural and urban France and include people with grievances beyond objections to the fuel duty.