The government has climbed down on plans to ban suspected rioters from using social networking websites in times of civil unrest.

The home secretary, Theresa May, told social networks at a meeting on Thursday that the government had no intention of "restricting internet services".

Research in Motion (RIM, the maker of BlackBerry), Facebook and Twitter were summoned to the meeting with May after David Cameron signalled a clampdown on the sites following the recent riots in England.

The social networks were poised to face down the government on its plans, which they warned could usher in a new form of online censorship in the UK.

However, government ministers sought to back away from the prime minister's comments and instead focus on how law enforcement could better use Twitter and Facebook in emergencies.

A Home Office spokeswoman described the meeting as constructive. May chaired the meeting with the Foreign Office minister Jeremy Browne, and members of the Association of Chief Police Officers.

The Home Office said in a statement: "The discussions looked at how law enforcement and the networks can build on the existing relationships and co-operation to prevent the networks being used for criminal behaviour. The government did not seek any additional powers to close down social media networks."

The possibility of banning suspected rioters from social networks was first raised by Cameron a fortnight ago when he vowed to do whatever it took to prevent a repeat of the riots and looting.

Hours before the meeting human rights groups sent an open letter to government ministers warning that powers restricting the internet could be "susceptible to abuse" and undermine free speech.

May is understood to have opened the meeting by immediately ruling out restrictive measures and indicating that it was a discussion about improving law enforcement online.

According to sources at the meeting, police acknowledged that they "needed to do more" with regard to learning how to use social media. The Metropolitan police are understood to have said they were "slightly behind" other forces when it came to Twitter and Facebook.

Surprisingly, RIM was not forced to explain how its BlackBerry Messenger service differed from other social networks, despite the system reportedly having played a pivotal role for the rioters.

A spokeswoman for Facebook said the discussion was constructive, building on work her firm already did to ensure Facebook was "one of the safest places on the internet". She said: "We welcome the fact this was a dialogue on working together to keep people safe rather than about imposing restrictions on internet services."

A Twitter spokeswoman said: "Governments and law enforcement agencies around the world use Twitter to engage in open, public, communications … we've heard from many that Twitter is an effective way to distribute updates and dispel rumours in times of crisis or emergency."

In a statement RIM said: "RIM continues to maintain an open, positive, dialogue with the UK authorities and continues to operate [within] UK regulations."

The Home Office meeting followed a study of riot-related tweets, compiled by the Guardian, that cast doubt on the rationale behind Cameron's proposal to bar suspect rioters from Twitter and Facebook.