The connection was particularly strong among overweight and obese children, said Quanhe Yang from the Centers for Disease Control and Prevention (CDC) in Atlanta, who worked on the study.
That's concerning because both high blood pressure and excessive pounds are risk factors for cardiovascular problems such as heart attacks and stroke down the road, researchers say.
"Our American diet clearly is very high in sodium," said Dr. Frederick Kaskel, chief of pediatric nephrology at Children's Hospital at Montefiore in New York, who was not involved in the research.
"Not only is the high sodium something to be avoided, but it is also indicative of an unhealthy diet," he told Reuters Health.
The results, released Monday in the journal Pediatrics, are likely to fan the hot debate over the health effects of salt.
While health authorities across the globe warn consumers to cut back on dietary salt, a number of recent studies have suggested that not getting enough salt can be as harmful as getting too much.
The salt industry has pounced on that research, saying the dietary guidelines for sodium intake are flawed and should be withdrawn.
The CDC study is based on national surveys of more than 6,200 children and adolescents aged 8 to 18. The youths had their blood pressure measured between one and three times and also reported their diet in the prior 24 hours.
On average, they ate 3,387 milligrams of sodium a day - considerably more than the 2,300 mg (about one teaspoon of salt) the government recommends as the upper limit.
According to previous data from the CDC, U.S. adults consume 3,466 mg of sodium per day by comparison.
"Kids are consuming as much sodium as adults, which far exceeds the recommended amount," Yang told Reuters Health, encouraging parents and others to "read the label when you go shopping and buy the food with the lowest sodium content."
Yang and his colleagues found that for every 1,000 mg of extra sodium in the children's diets, there was a one-point rise increase in blood pressure. Among overweight and obese kids, each 1,000 mg of sodium was tied to a blood pressure increase of 1.5 points.
In adults, high blood pressure is defined as at least 140 mm Hg (the top, or systolic, number) or 90 mm Hg (the bottom, or diastolic, number). Doctors also talk about "pre-hypertension," which is defined as a top number between 120 mm Hg and 140 mm Hg or a bottom number between 80 mm Hg and 90 mm Hg.
The potential health effects of the small blood pressure variations seen in the study are not clear. But Kaskel said they could spell trouble later on.
"The antecedents of adult cardiovascular disease are seen early on in the pediatric age group," he said. "We shouldn't underestimate the potential harms of a 1-mm increase in systolic blood pressure."
The new study doesn't prove that higher dietary salt intake directly increases blood pressure, however, although other research shows that is theoretically possible.
"Many times the higher intakes of sodium may simply be a marker of a higher intake of fast food and processed foods," said nutritionist Lauren Graf of Children's Hospital at Montefiore.
She added that several ingredients in such foods, including fructose, have been tied to higher blood pressure.
Dr. Michael Alderman of the Albert Einstein College of Medicine in New York cautioned that it's not clear that cutting back on sodium will do most kids any good.
"There is nothing in this paper - and there is no information that I'm familiar with - that suggests reducing sodium intake is of value for people eating an average of 3,400 milligrams of sodium a day," he told Reuters Health.
Alderman said he has been an adviser to the Salt Institute, which represents the industry, and received $750 from the group in 1995. He said he has no ties to the group today.
Graf said bread is the biggest source of dietary sodium in the U.S., adding that deli meats also contain a lot of the ingredient. Eating a healthy diet - including whole grains, vegetables, fruits, and fresh fish and meats - will automatically reduce sodium intake, she noted.