Google may co-operate more closely with Facebook and Twitter and believes there is room for multiple social networks as it rolls out its own Google+ product, according to executive chairman Eric Schmidt – but the two rivals appear to disagree.

He said the company will co-operate fully with American antitrust regulators but will not let the formal antitrust probe, launched last month, distract or disrupt its strategy.

Speaking at the Allen & Company media conference in Sun Valley, Idaho, Schmidt – who handed over the job of chief executive to co-founder Larry Page in April after 10 years, and now oversees government affairs – said it was too early to say how Google+ was faring. But one key indicator was the number of people clamouring to be part of the limited group currently using the social networking site, which launched in trial mode last week.

One of the more popular features on Google+, especially with younger users, was online video chat, he said.

Singling out two services where Google+ can now be viewed as a competitor, Schmidt said he would "love to have deeper integration with Twitter and Facebook."

But that is not evident in the reactions of the two companies. Google's "realtime search" deal with Twitter recently expired after 18 months, leading to the demise of the search feature in which recent tweets related to a search topic appear in Google search results. Despite "a substantive and lengthy discussion," the companies couldn't agree on terms, Schmidt said. Google will relaunch the realtime service with input from "a number of sources" – although it already drew from 17 different sources, including Quora and Facebook fan pages – the company said. That will almost certainly including Google+.

The realtime search provision on Google was one of the first deals struck by Twitter in October 2009. It signed a similar deal with Microsoft to provide the same facility on its Bing search site. That still continues; it is not known whether the deal with Bing has been renewed, or was for a longer period initially.

Facebook, meanwhile, has blocked an extension for Google's Chrome browser which would have let people grab the data about their Facebook friends, including emails and phone numbers, to import them to other networks. Facebook acted to block the extension it by removing emails from its mobile site, which the extension used to gather the data.

Google's overtures to Facebook to discuss letting Google+ users import Facebook friends led nowhere, Schmidt said.

Schmidt laid out a future with multiple sources of online identity and multiple social networks, even as detractors say Facebook's service, with around 750 million users around the world, is too entrenched to allow for serious competition.

Schmidt said Google executives – though not he himself – had discussed the recent hacking of email accounts with Chinese officials.

Google last month revealed a major hacker attack that it said originated within China. It said hackers tried to steal the passwords of hundreds of Google email account holders, including those of senior government officials, Chinese activists and journalists.

"We tell the Chinese what we know ... and then they publicly deny their role. That's all I have to say about that," Schmidt said.

Meanwhile, the US Federal Trade Commission (FTC) has started a formal review of Google's business, raising concerns among investors about a lengthy, distracting probe and potential legal action.

The FTC is expected to address complaints from Google's rivals that its search results favour the company's own services. Google, which runs an estimated 69% of web searches worldwide, can make or break a company depending on its search ranking.

Some worry that Google's desire to stand firm against government intrusion – as with its protests against Chinese censorship of search results – will trigger a long battle that ultimately does more damage than a quick settlement.

"We've had some meetings internally, [but] we haven't changed anything," Schmidt said.