The French president, François Hollande, has been accused of caving in to reactionaries after shelving plans to change family law this spring.

Supporters of the reforms denounced Hollande and his Socialist government as "political cowards" after the announcement on Monday that the bill would not be introduced this year, as promised.

The legislation comprised a raft of measures widely viewed as positive and constructive, including giving step-parents a legal status, regulating custody and visitation rights and maintenance payments between divorcing couples, introducing mediation before divorce, making adoption easier and allowing adopted children to trace their real parents.

Rightwing and ultra-conservative groups saw the reforms as an attack on traditional values. On Sunday, there were demonstrations in Paris and Lyon in "defence of the family" by protesters opposed to same-sex marriage, which has been legal in France since last year.

Anne-Cécile Mailfert, of Osez le Féminisme (Dare to be Feminist), said: "The government is afraid of reactionaries, and in giving in to them they've let them win. It's a sign of cowardliness. People voted for the left because of its social projects." She said the government's retreat would "reinforce the enemies of social progress".

Ministers said the bill had not been dropped but only postponed until 2015. But critics described the U-turn as a farce.

Hollande's popularity is already at a historic low, and the far-right Front National is expected to make gains in approaching European and local elections.

The women's rights minister, Najat Vallaud-Belkacem, suggested the decision had been forced by the "hysteria" surrounding the proposed bill.

She said the government needed more time to "develop the family law project and create more calm conditions for the necessary consultation".

Organisers of the protest group Manif pour Tous (Demo for All), which brought more than 100,000 people on to city streets on Sunday in defence of what it described as the traditional family, claimed a victory after the announcement.

It has accused the government of being family-phobic and argues that children have a right to a mother and a father. It is also vehemently opposed to same-sex couples being given access to IVF treatment or surrogacy in order to have children, a measure some Green party and Socialist MPs wanted added to the bill.

Sergio Coronado, an MP for the Europe Écololgie les Verts (EELV) party, which has two ministers in Hollande's centre-left administration, said the government's retreat was ridiculous. "To give satisfaction to a movement that is so reactionary is catastrophic," Coronado told Le Parisien. "The government seems to think that in giving in they will calm this movement but all they have done is fed it and given the impression that the street can dictate the parliamentary agenda."

Another EELV MP, Noël Mamère, said the decision was a sign of the government's "great vulnerability as well as its lack of political will to address social subjects that need reforming".

Even the mainstream opposition UMP party was critical. Christian Jacob, head of the UMP parliamentary group in the national assembly, accused the government of going from "a muddle to a panic".

Publication of the family law had already been postponed twice before Monday's announcement. It was originally due to be unveiled in 2013 before being put off until April, shortly before municipal elections.