A growing number of US children say they have been picked on via text messaging, including having rumors spread about them or been threatened, a study said.

Of more than 1,500 middle school and high school students surveyed in 2008, 24 percent said they had ever been "harassed" by texting -- up from 14 percent in a survey of the same students the year before, according to findings published in Pediatrics this week.

"Harassment" meant that peers had spread rumors about them, made "rude or mean comments", or threatened them.

Outright bullying, which was defined as being repeatedly picked on, rose to 8 percent of students surveyed from just over 6 percent the year before.

Researchers, led by Michele Ybarra of Internet Solutions for Kids Inc in San Clemente, California, told Reuters Health that the findings suggest that attention needs to be paid to children's text-messaging, but that parents need not be alarmed.

"This is not a reason to become distressed or take kids' cellphones away. The majority of kids seem to be navigating these new technologies pretty healthfully," she said.

The study included 1,588 10- to 15-year-olds who were surveyed online for the first time in 2006. The survey was repeated in 2007 and 2008, with about three-quarters of the original group taking part in all three.

It did not say why the results of the survey completed in 2008 were released now.

When came down to Internet-based harassment, as opposed to texting, there was little change over time. By 2008, 39 percent of students said they'd ever been harassed online, with most saying it had happened "a few times". Fewer than 15 percent said they'd ever been cyber-bullied.

Even when students were picked on, most seemed to take it in their stride, which researchers said was a good sign.

Of those who said they'd been harassed online, 20 percent reported being "very or extremely upset" by the most serious incident, down a bit from 25 percent in 2006.

Ybarra and other experts said that the main message for parents was to try to help their children manage their relationships in a healthy way, since the issue was fundamentally a relationship problem.

Cyber-bullying still remained a smaller problem than the old fashioned kind, they said.

"Meanness and bullying are still much more likely to occur face-to-face," David Finkelhor, who directs the Crimes Against Children Research Center at the University of New Hampshire in Durham said.