What the world needs now is a Web-enabled toothbrush.

That part is clear to several oral-hygiene companies. What they can't agree on is who was first to put teeth into the smartphone.

The giant Procter & Gamble Co. last week demonstrated what it calls the 'World's First Available Interactive Electric Toothbrush.' It links with a smartphone and records brushing habits, while an app gives mouth-care tips alongside news headlines.

A French startup bristles at that claim. Paris-based Kolibree also last week touted the 'World's First Connected Electric Toothbrush.' The 12-person company says it was first because it showed its device, which also records dental data via smartphone, in January.

Kolibree Chief Executive Thomas Serval last week trekked to the yearly Mobile World Congress here to show off his brush a few minutes' walk from P&G's 'connected bathroom' display.

'To be honest, I wasn't going to come here,' he says. 'But I wanted to make sure no one could say they are 'first' when they are not.'

Neither company questions whether there is a place for a digital dental device above the sink.

'There are people who are very passionately waiting for it,' says Michael Cohen-Dumani, associate marketing director for P&G's Oral-B electric toothbrush business.

'I truly believe that 10 years from now,' he says, 'it's going to be hard to think you didn't have something like it.'

Not everyone is champing at the bit. 'It's one of those things you think are great at first but never actually buy,' says Karina Clarke, a 34-year-old Paris real-estate agent. The idea, she says, seems like 'a microwave you put in your mouth.'

This race to wire the world's jaws is playing out in one of tech's buzziest arenas: the so-called Internet of things. Giants like Google Inc., which recently bought a networked-thermostat maker called Nest, are investing, as are smaller startups. New products include smart socks (to measure running form) and connected water bottles (to gather water-consumption data.)

'We're just at the beginning of seeing a bunch of really ridiculous products that tie pretty much anything to a smartphone,' says Stacey Higginbotham, who writes about the Internet of things for tech website Gigaom.

The roots of the Internet toothbrushes stretch back at least two years. P&G was researching how to improve its electric-toothbrush line, which already offered external timer screens to encourage longer brushing, Mr. Cohen-Dumani says. The jump to smartphones was a logical step.

Around the same time, Kolibree's Mr. Serval was looking for ways to encourage his kids to brush more and hit on the idea of a connected brush, he says.

Mr. Serval is a serial investor in the world of connected devices. He started and sold a connected barcode-scanner company and recently bought into a French startup that plans to bring out an Internet-connected e-cigarette.

Kolibree is betting on sensors and analytics to improve the daily oral-hygiene ritual. Its sonic toothbrush, called the Kolibree, includes nine motion sensors and an algorithm designed by five mathematicians to identify which quadrant of the mouth a user is brushing, Mr. Serval says.

Kolibree is designing its brush so anyone, from dentists to game developers, can build applications that tap into its data. 'We are kind of geeks going into the dental industry,' Mr. Serval says. 'We want to use data to reinvent the way people brush their teeth.'

P&G is leaning on its history. The company's Oral-B brand offered its first electric toothbrush in 1963. The mobile app with P&G's toothbrush -- it will be part of the Oral-B SmartSeries line -- tells avid users how long to spend on each corner of the mouth.

Some features are industrial secrets. Mr. Serval gives few details about what sensors are inside his Kolibree brush, saying he wants to avoid tipping off competitors. He declines to show the final version of the smartphone app that operates his toothbrush, wanting to keep its design a secret.

'They are not stealing. I want to be very, very clear about that,' Mr. Serval says of P&G. 'But there are some ideas and even some worldviews in what they are doing that are very close to my pitch.'

When Oral-B promoted its new brush as the first available in a news release ahead of the Mobile World Congress, Kolibree noted that it had announced its brush during January's Consumer Electronics Show in Las Vegas.

P&G started development of its app and brush long before Kolibree's January unveiling, P&G's Mr. Cohen-Dumani says. 'It's impossible to start or copy a product like that in a month,' he says. 'It is a coincidence maybe that we had the same idea.'

P&G says its will be the first connected electric brush available to consumers. 'Our competitors have some prototypes,' says Mr. Cohen-Dumani, 'and we are excited to see how they come along.'

P&G says its toothbrush will be available in limited quantities in Germany in May before a global rollout begins in June. It recommends a $219 retail price tag in the U.S.

Kolibree says its brush will be available in limited quantities in June and widely by fall. It expects a price of $100 to $200.

Neither toothbrush will technically be the first on sale to track teeth on an app. Beam Technologies, a Louisville, Ky., startup, has been shipping a connected toothbrush since January 2013.

But its brush is manual, not electric like Kolibree's and P&G's. Beam Chief Executive Alex Frommeyer admits that leaves the first-toothbrush question open to interpretation.

'To some extent, it's how you play the marketing game and the semantics involved,' he says. 'But it definitely bothers me.'

Competition among Web-enabled toothbrushes is set to continue. Beam plans a powered brush. Kolibree is working on a companion device with sensors to identify dental disease. P&G is exploring adding 'detection and motion-sensing' to future versions.

But 'until robots can brush for you,' P&G's Mr. Cohen-Dumani says, 'you still have to do that part yourself.'