Tens of thousands of Spaniards protested on Sunday against a new labour law which hands more power to employers by making it cheaper to fire workers and easier to restrict wage hikes.

The demonstrations were the first since unions called a general strike for March 29 and add to a growing number of street protests against government reforms and spending cuts aimed at putting Spain's finances back on track.

Union organisers said as many as half a million people attended the peaceful marches in 60 cities, where protesters beat drums and waved red union flags, although police gave no official estimate.

Spain has the highest unemployment rate in the European Union at 23 percent and the government predicts this will hit a record high of 24.3 percent this year. Spain accounts for nearly a third of all the jobless in the euro zone.

The centre-right government says measures like cutting severance pay to 33 days for every year worked from 45 days and restricting inflation-linked salary hikes will bring flexibility to Spain's rigid labour market.

The government is desperate to show Brussels it is serious about enforcing unpopular structural reforms and spending cuts aimed at keeping its budget under control.

But protesters in Madrid said the measures wrecked workers' rights.

It's damaging for workers, it makes it easier to fire people, it benefits employers -- they're laying us off across the public sector, said Irene Jimenez, a 29-year-old health worker on the latest of a series of three-month contracts.

The reform would not help Spain's unemployed, public sector employee Jose Javier Rodriguez, 53, said.

It's absurd to think you're going to bring down unemployment by making it easier to fire people, he said.

The March 29 general strike is the first since September 2010 when unions balked at a watered-down labour reform enforced by the previous Socialist government.

The 2010 strike had limited impact aside from disrupting transport and factories.

Around three-quarters of Spaniards do not believe the labour reform will help create jobs, according to a recent poll. However, 67 percent believe a general strike will not help matters and may make the situation worse.

(Editing by Michael Roddy)