Speaking in a televised address to the nation, Mr Macron said that the anger of protesters was "deep, and in many ways legitimate".
The yellow vest protests began in November against a rise in fuel taxes - which Macron retreated from last week - but mushroomed into other, sometimes contradictory demands.
The beleaguered leader said "no anger justifies" looting shops or attacking police, adding that both threaten France's cherished liberty.
The minimum wage will be increased by 7% - and the cost of this increase will be met by the government rather than employers.
In the government official stressed that the final decision on the mechanisms for the implementation of the ideas the President has not yet accepted and now undergoing the process of "fine-tuning of economic mechanisms". "I might have hurt people with my words".
In another move to appease protesters' anger, Macron said he would do away with all wage taxes on overtime work.
French President Emmanuel Macron has acknowledged he's partially responsible for the anger that has fueled weeks of protests in France, an unusual admission for the leader elected a year ago. Macron has previously said he wants to reform and strengthen the eurozone single currency area, urging member states to stick to the rules.
For Laurent Joffin at the left-wing Liberation newspaper, Macron is "betting on a fall in support for the "yellow vest" protesters".
Oil prices rise as equities rally, Libyan supply outage continues
West Texas Intermediate crude weakness returned as concerns for slower global growth stemmed from soft Chinese data. International Brent crude oil futures LCOc1 were at $60 per barrel at 0746 GMT, up 3 cents from their last close.
"This would weaken us, we need to create jobs", he said, according to the BBC.
Macron this week gave in to some of the protesters' demands for measures to help the poor and struggling middle classes, including scrapping a planned increase in fuel taxes and freezing electricity and gas prices in 2019.
Macron, who has been in power for the past 18 months, on Monday held four hours of crisis talks with government ministers, parliamentary leaders, business and labour representatives and regional officials.
President Trump weighed in several times by Twitter over the weekend, blaming the French unrest on reaction to the costs of climate change policies and the Paris climate accord that Mr. Macron has championed.
He denounced the protest-associated violence that led to hundreds of injuries, more than 1,000 arrests, and the ransacking of stores in some of Paris's richest neighborhoods.
The Federation of Commerce and Distribution, an industry group representing many of France's largest chains, estimates retailers have suffered more than 1 billion euros ($1.1 billion) in lost revenues, with toy, clothing and food sales among the sectors hit. But the protests continued as "Act 4", as Yellow Vests called the latest round, took place over the weekend. French Finance Minister Bruno Le Maire said the disruptions have lowered gross domestic product by one-tenth of 1 percent in just a month.
The Interior Ministry said 136,000 people participated in Saturday's protests, similar to the previous week's numbers. "If I fought to shake up the political system, it's because I believe in this country more than anything else".
Spokespeople for the far-right National Rally and far-left France Unbowed, the two parties that have tried most energetically to piggyback on the protests, also said the measures were inadequate, as did the head of one of France's two largest unions.