The proposals presented to the first meeting of a reshuffled cabinet appointed Wednesday are designed to allow the lifting of the state of emergency that has been in place since the November 2015 attacks in Paris.
The state of emergency has been extended five times since it was introduced by the then Socialist government in response to the gun and bomb rampage that left 130 people dead.
The current provision expires in mid-July, when Macron's new centrist government is expected to extend it again until November 1 while the new law is prepared.
The legislation has received the go-ahead from France's top administrative court despite concerns from rights groups including Amnesty International and Human Rights Watch that it will enshrine into law draconian powers allowed under the state of emergency.
Amnesty complained last month that French authorities were abusing anti-terrorism measures by using them to curb legitimate protests.
France has faced a string of jihadist attacks since 2015, with the threat underlined on Monday when a man rammed a car laden with guns and gas canisters into a police van on Paris' Champs-Elysees avenue.
The driver of the car, 31-year-old Adam Djaziri, died in the attack but no one else was injured.
Paris prosecutor Francois Molins told a press conference Thursday that all evidence suggested Djaziri had intended the car to explode.
He had mailed a letter to his family just before the attack saying he had wanted to travel to Syria and complaining he had been stopped from doing so "by apostates against the Islamic State".
Djaziri had been on a watchlist for radical Islamists after attracting the attention of authorities by making several trips to Turkey -- a route used by many European jihadist fighters heading to Syria in recent years.
Authorities have launched a review of gun ownership after it emerged that Djaziri, who practised shooting as a sport, had been legally allowed to possess firearms despite being on the watchlist since 2015.
Speaking from Brussels, where he had been attending a European summit, Macron admitted there had been a "malfunction" in the system and said changes to the law would be made to allow more thorough background checks.
Four members of his family, who lived in the Paris suburbs, were detained for two days before being released on Wednesday.
'Strikes right balance'
The new anti-terror law would give French authorities greater powers to act to protect an event or location thought to be at risk from attack, without first seeking permission from the courts.
Local authorities could, for example, decide to put in place a security cordon and carry out bag checks and searches using private guards without seeking approval beforehand.
The draft law would also allow places of worship thought to be promoting extremism to be shut down for up to six months.
Prime Minister Edouard Philippe argued it struck the "right balance" between respecting freedoms and reinforcing security.
"We want to guarantee security and we want to do so while respecting the law and the constitution," he told French news channel TF1 on Wednesday.
Interior Minister Gerard Collomb, who retained his job in Wednesday's government reshuffle, said the Champs-Elysees attack was a timely response to those questioning the necessity of the new law.
"You can see that the state of France today necessitates it," Collomb said, speaking on Monday.
"If we want to effectively ensure the security of our citizens, we must be able to take a certain number of measures."
Since the large-scale attacks in Paris in 2015 and in Nice the following year, which were both claimed by the Islamic State group, France has seen a series of smaller jihadist assaults, mostly aimed at security forces.
A known extremist shot dead a policeman on the Champs-Elysees in April, just days before the first round of the presidential election..