Google has opened its ambitious social networking site Google+ to the public, having attracted more than 20 million users for aits 12-week invitation-only trial.

The public launch marks a significant moment in the search giant's challenge to Facebook, which has almost 800 million active users around the world, and the messaging service Twitter, which has more than 100 million members.

Unlike Facebook, where you have to be a "friend" with a counterpart, or Twitter, where "followers" and even unregistered visitors to Twitter's website can typically see anything that someone tweets, Google+ uses "circles", where a posting cannot be shared more widely than its creator wants. At its broadest, that can be completely public – but it can also be a circle only of one person, or just family or close friends.

Google+ also breaks with the brevity of Twitter, allowing users to post messages of unlimited length to any number of friends.

More than 1bn items have been shared on the new social network since its launch, said Vic Gundotra, Google's senior vice-president of engineering, in a post on Google's official website on Tuesday. He announced nine new features for the fledgling site, including the ability for users to video chat using Google+ on compatible mobile phones. Users will also be able to record and broadcast video chats for friends to watch, and complete tasks with friends, he said.

Google also introduced a search feature for the site.

The search engine giant's latest major social networking project got an underwhelming response from critics on its launch on 29 June, but the service quickly attracted millions of users, according to calculations. Google has tried to build worldwide social networks before, with Orkut – which succeeded in Brazil and India, but flopped elsewhere – and with Buzz, which used people's email accounts to construct a "social network" on the fly. However privacy flaws in Buzz, which attracted a barrage of complaints from users whose contacts were inadvertently exposed on the site, led to an investigation by the US Federal Trade Commission, in turn leading to a 20-year oversight ruling on Google and the privacy of its products.

Chief executive Larry Page indicated big ambitions for Google Plus when discussing the company's financial results in July. "Our goal at Google+ is to make sharing on the web like sharing in real life, as well as improve the overall Google experience," he said. "Circles lets you choose with precision who you're sharing with; not surprisingly this has been very well received, because in real life, we share different things with different people. Hangouts allows for serendipitous interactions – like in real life, when you run into a few friends. It gives you seamless and fun multiuser video, and it's really amazing."

Gundotra said in June that Google+, which took more than a year to develop, is the answer to flaws in existing social networks, which he described as "sloppy", "scary" and "insensitive". Buzz was launched in February 2010.

"For the past 12 weeks we've been in field trial, and during that time we've listened and learned a great deal," Gundotra said. "We're nowhere near done, but with the improvements we've made so far we're ready to move from field trial to beta, and introduce our 100th feature: open signups. This way anyone can visit google.com/+, join the project and connect with the people they care about."