Participants in the study lost weight on both diets
A low-carbohydrate diet like Atkins is better at cutting blood pressure than weight-loss pills, say US doctors.
Twice as many people on the low-carb diet lowered their blood pressure compared to those taking the drug, orlistat.
The study, in the Archives of Internal Medicine, found the two approaches achieved equal weight loss and those who received counselling lost the most.
The study looked at 146 people who had a range of health problems.
Many obese and overweight people are advised to lose weight to help them lower their blood pressure.
The researchers from the Veterans Affairs Medical Centre and Duke University Medical Centre say nearly half (47%) of those in the low-carbohydrate group were able to reduce or cut out their blood pressure medication, compared with around one fifth (21%) of those on orlistat plus a low-fat diet.
The two strategies were equally effective at improving cholesterol and glucose levels, as well as waist size and weight loss.
The lead author, Dr William Yancy, from Duke University Medical Centre, said: "The findings send an important message to people with high blood pressure who are trying to lose weight.
"While weight loss typically induces improvements in blood pressure, it may be that the low-carbohydrate diet has an additional effect."
"It's important to know you can try a diet instead of medication and get the same weight loss results with fewer costs and potentially fewer side effects."
The participants were offered regular group weight loss counselling throughout the study.
Those who attended 15 or more sessions over the course of the year lost significantly more weight than the rest, shedding almost 15% of their body weight.
Orlistat is marketed under the brand names Alli and Xenical.
Alli is available over the counter in the UK at half the dose used in the study.
The pill works by stopping some dietary fat from being digested and absorbed into the body.
It is supposed to be used alongside a reduced-calorie, lower-fat diet.
The drug is not recommended for people with a body mass index of less than 28.
The British Heart Foundation said: "This small study reinforces the message that weight loss in obese individuals will have a significant impact on the risk factors associated with cardiovascular disease.
"Identifying that you need to lose weight, finding a dietary approach that suits you individually combined with a regular physical activity programme, will help to reduce your risk of coronary heart disease and stroke."