MOSCOW (Reuters) - Hundreds of Russians protested in Moscow on Tuesday against new anti-terrorism legislation approved by President Vladimir Putin that critics say will curb basic freedoms and make it easier for the authorities to stifle dissent.

In Moscow's wooded Sokolniki park, rights activists gave speeches criticizing the new legislation while some people carried banners reading "Down with political repression" and "Repression is fear before your own people".

Opposition leader Alexei Navalny urged those present to draw inspiration from protests against Putin in 2011-12. "We should return to the streets," Navalny shouted to the crowd. "We'll make Russia free.

There was a light police presence at the protest which had been given the go-ahead by officials.

The new package of anti-terrorism laws, championed by prominent lawmaker Irina Yarovaya from the pro-Kremlin United Russia party, was signed into law by Putin in July.

It toughens penalties for extremism, introduces prison sentences for failure to report a grave crime, a Soviet-era practice, and increases the number of crimes for which Russians as young as 14 years old can be prosecuted.

It also obliges network operators to store recordings of phone calls, images and messages of their users for half a year as well as data on those calls for a longer period.

Activists have called the changes repressive and said they could be used to pressure Kremlin opponents ahead of a parliamentary election in September. New York-based Human Rights Watch has called the new laws draconian.

"The Yarovaya Laws will ... severely curb people's right to exercise free expression and other fundamental freedoms in Russia," it said in a June statement.

Russian telecoms firms have said the new laws entail huge additional costs. The share prices of firms such as MTS and MegaFon tumbled after Putin approved the law last month.

(Reporting by Alexander Winning and Gennady Novik; Editing by Andrew Osborn and Janet Lawrence)