The "yellow vest" movement, which originally erupted over anger at fuel tax increases, has ballooned into a wider protest over rising costs of living and a perceived disregard by Mr Macron for the problems facing rural and small-town France.
Macron is a 40-year-old former investment banker and economy minister.
Mr Griveaux also said the government would permanently end the fuel tax hikes planned for January if no agreement were reached at the end of the consultation period called by Prime Minister Edouard Philippe.
The FNSEA farmers' union said it would fight to help French farmers earn a better income but would not officially be joining forces with the "yellow vests" - protesters wearing the high-visibility vests that French motorists are required to keep in their cars.
"This violence must end", Philippe said. Pressure has been mounting after the grassroots "yellow vest" movement degenerated into fiery street clashes and vandalism in Paris over the weekend, leading to scores of injuries and arrests.
Three weeks of demonstrations left four people dead and were a massive challenge to Macron.
Rescinding the fuel tax hike was the main demand of the demonstrators, alongside a higher minimum wage and the return of a wealth tax on high-earners which was abolished previous year.
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).
But his office said he told ministers he would stick to his decision to cut a "fortune tax" on high-earners - a move which has infuriated many protesters. "We want Macron and his entire government to resign".
"The Paris Agreement is fatally flawed because it raises the price of energy for responsible countries while whitewashing some of the worst polluters". People want "the baguette", not crumbs, and will take to the streets again on Saturday, he said.
On Sunday, President Emmanuel Macron considered declaring a state of emergency as he met security chiefs seeking a way out of nationwide protests after rioters turned central Paris into a battle zone and vandalized the Arc de Triomphe monument. Some 4,500 police officers were deployed to deal with about 10,000 protesters in Paris alone.
Paris Saint-Germain's home Ligue 1 football match against Montpellier on Saturday has already been called off, as has an electro music festival in the city centre.
French President Emmanuel Macron assesses the damages of the "Yellow Vests" protest earlier on the week.
The president - who enjoyed a landslide election victory previous year - now has an approval rating below 30%.
Since returning from the G-20 summit in Argentina over the weekend, Macron's actions have done little to reassure protesters that he is listening to their concerns.
To be sure, Macron's recent efforts to combat "climate change" and reduce France's dependence on "fossil fuels" by levying a new tax on gasoline and other household fuels is not the only reason the French are protesting, but fuel tax is the "straw that broke the camel's back".
Immediately after coming to power in 2017, Macron pushed through tax cuts for entrepreneurs and high-earners - an "original sin" for his critics.