The French prime minister, Édouard Philippe, warned lawmakers to prepare for a long battle over proposed changes to the pensions system, as more than 300,000 people took to the streets on Tuesday as a transport strike to ran into a second week.

Rail-workers, teachers, air traffic controllers, doctors, national library staff and even ballet dancers marched through Paris and other cities to protest against the biggest overhaul of the French pension system since the post-war period.

Numbers were down on last week’s street protests when at least 800,000 people took part in one of the biggest demonstrations of trade union strength in a decade. But unions said the nationwide transport strike would continue.

Facebook Twitter Pinterest Commuters wait on a platform at the Gare du Nord RER station in Paris on Tuesday morning. Photograph: Eric Gaillard/Reuters

Philippe is expected to announce the details of the government’s pensions proposals on Wednesday. But he downplayed the prospect of a speedy breakthrough in the dispute, saying there would be “no magic announcements” that would bring protests to a sudden halt. However, he suggested the pension changes could be gradual.

Emmanuel Macron, the pro-business president who has promised to deliver the biggest “transformation” of the French social model and welfare system in 50 years, sees his pension reforms as a key test. He has staked his political credibility on refusing to buckle in the face of street protests. Backing down would be to risk losing his support-base. But demonstrators said they feared France’s social safety net was being unpicked.

Q&A Who are the gilets jaunes? Show Hide A grassroots citizens’ protest movement began in early November 2018 against a planned rise in the tax on diesel and petrol, which Emmanuel Macron insisted would aid the country’s transition to green energy. A poll at the time found that the price of fuel had become France’s biggest talking point. The movement was named “gilets jaunes” (yellow vests) because protesters wear the fluorescent yellow high-vis jackets that all motorists must by law carry in their cars. But what began as a fuel tax protest morphed into a wider anti-government movement. Unlike previous French protest movements, it sprang up online through petitions and was organised by ordinary working people posting videos on social media, without a set leader, trade union or political party behind it. Angelique Chrisafis in Paris

The government is concerned that protestors have taken to the street not just in big cities, but in small provincial towns, echoing the mood of the gilets jaunes (yellow vests) anti-government protests earlier this year. People are angry not only with pensions but low salaries, worsening prospects, the state of public services and what one demonstrator called “the feeling of being forgotten”.

One local MP for Macron’s party said it would be hard to tackle a protest movement that spread from pensions to several different grievances at once.

Facebook Twitter Pinterest Commuters wait at Gare de l’Est train station in Paris. Photograph: Christian Hartmann/Reuters

Guillaume Bouslah, 32, a freight rail worker from the Paris suburbs, said: “No one is talking about stopping the strike. I’ve already lost a week’s pay. If we have to continue, we’ll keep going, we feel supported by other professions and the public. The government clearly wants to boost private pension funds. Surely France should be defending its unique social model, not breaking it?”

Sophie, 48, a primary teacher in Essonne said: “The unease runs deep: a lack of staff in schools, low salaries and the feeling that public services are under attack.”

Across the country, transport turmoil continued with trains at a virtual halt, some flights grounded, 10 lines of the Paris metro closed and more than 180 miles (300km) of traffic jams on roads around Paris by 7am.

Facebook Twitter Pinterest Union members and employees of the Paris transport network RATP block a bus depot in Les-Pavillons-sous-Bois near Paris. Photograph: Lucien Libert/Reuters

In the greater Paris area, where more than 9 million people depend on an already overburdened public transport system each day, there were dangerous crushes on packed platforms.

The government argues that unifying the French pensions system – and getting rid of the 42 “special” regimes for sectors ranging from rail and energy workers to lawyers and Paris Opera staff – is crucial to keep the system financially viable as the population ages. But unions have claimed the changes are an attack on fundamental workers’ rights, and fear people will have to work longer for smaller pensions.