"The priority now is the battle against the crisis, for employment and to tackle unemployment," Castex told reporters after his first meeting with union representatives since becoming prime minister this month.
Castex said the reform, which includes raising the retirement age by two years to 64, would not be scrapped.
A deferment until after the 2022 presidential elections might defuse union and voter concerns but would undermine Macron's already-weakened credibility as a reformer.
The reform is central to Macron's ambition of creating a more flexible and competitive labor force. But trade unions who argue that it will erode hard-earned benefits and leave pensioners worse off.
Surging Cases in France's Brittany Region
The popular tourist region of Brittany is seeing a spike in the reproduction rate of the Covid-19 virus based on government data.
The news indicates the virus transmission is gaining momentum in France.
The French government sped up plans to make wearing face masks mandatory in enclosed public spaces on Thursday.