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.
Fuel taxes had been set to rise on January 1.
Griveaux stressed that the tax hikes could be scrapped permanently if no agreement was reached during consultations over the next six months. He also announced that electricity and natural gas prices will not increase before May 2019.
"It's a first step, but we will not settle for crumbs", said Benjamin Cauchy, a self-proclaimed protest leader.
A protester wearing a yellow vest, the symbol of a French drivers' protest against higher diesel fuel prices, holds a flag near burning debris at the approach to the A2 Paris-Brussels Motorway, in Fontaine-Notre-Dame, France, December 4, 2018.
Police warned of potential violence during demonstrations in Paris on Saturday, with one small security forces union threatening a strike.
Mr Macron and Prime Minister Edouard Philippe's popularity ratings hit new lows as the "yellow vest" protests gathered speed, according to an Ifop-Fiducial poll.
Many are also anxious after Agriculture Minister Didier Guillaume said Wednesday that measures aimed at improving their negotiating power with distributors would be delayed as the government grapples with the "yellow vest" movement. Cars were overturned and burned, while French police and gendarmes responded with water cannons and tear gas.
Last weekend, more than 130 people were injured and 412 arrested in rioting in the French capital. The former investment banker, who has pushed pro-business economic reforms to make France more competitive globally, is accused of being the "president of the rich" and of being estranged from the working classes. He has promised to reform France's economy and increase economic growth.
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She added, "The global community can not keep turning a blind eye every time Iran blatantly ignores Security Council resolutions".
While understanding that the nation wants taxes to be lowered, Phillipe cautioned that such a move would result in fewer benefits for French citizens. The yellow vest protesters have called him "president of the rich".
Turnout for the protests had fallen from about 280,000 three weeks ago to 136,000 last Saturday, with some of the violence, auto burning, spray painting and damage to Paris' historic monuments alienating supporters. The tax increase has been described as an effort to move France further to renewable energy sources.
Political opponents of the government called Philippe's announcement Tuesday too little, too late. Macron's office said it had "no comment" on Trump's tweets.
Mouraud told protesters to seize on Macron's weakness and demand other perks, such as a minimum wage hike.
"The protesters seem wholly uninterested in party politics", Poirier wrote in the New York Times last week. "I'm calling this government to resign", Valette said.
Some officials, however, hope that the lack of clear leadership will lead the movement to break apart.
Eric Drouet, one of the movement's most famous instigators, called for a "return to Paris" on Saturday, "near the places of power, the Champs-Élysées, the Arc de Triomphe, Concorde". George Grow was the editor.
"What we are asking of you Mr Prime Minister, is not a postponement".