The new plan includes a voluntary target for manufacturers to cut sugar in children's food and drink by 20%, and a drive for every primary school child to exercise for an hour a day.
The British Medical Association called the 20% target "pointless" and said ministers had "rowed back" on promises.
A food industry body said manufacturers were making progress in cutting sugar.
The government's plan asks the food and drink industry to cut 5% of the sugar in products popular with children over the next year.
It says the ultimate target is a 20% sugar cut, with Public Health England monitoring voluntary progress over the next four years.
Officials say this reduction in sugar could also be achieved by making portions smaller, for example.
The plan also calls on primary schools to deliver at least 30 minutes of physical activity a day and to help parents and carers ensure children get the same amount at home.
School sports will also get more funds - boosted by a tax on sugary drinks to come into force 2018.
The government says the tax - announced five months ago - will also add £10m a year to school breakfast clubs.
The childhood obesity strategy also says:
- Public Health England (PHE) will set targets for sugar content per 100g, and calorie caps for certain products
- PHE will report on whether the industry is reducing sugar content through the voluntary scheme. If insufficient progress is made, the government will consider "whether alternative levers need to be used"
- A new voluntary "healthy schools rating scheme" will be taken into account during school inspections
The BMA said the plan omitted many measures backed by health experts, such as curbs on TV ads and cheap deals on junk food.
Professor Parveen Kumar, chairwoman of the BMA's board of science, said the government had "rowed back on its promises by announcing what looks like a weak plan rather than the robust strategy it promised".
"Although the government proposes targets for food companies to reduce the level of sugar in their products, the fact that these are voluntary and not backed up by regulation, renders them pointless," she said.
Ian Wright, of the Food and Drink Federation, said: "Soft drink companies are already making great progress to reduce sugars from their products, having achieved a 16% reduction between 2012 and 2016.
"Indeed, many individual manufacturers have a proud track record of reformulation to remove salt, fat and sugar from food and drinks and this work will continue."
He said the target to reduce sugar was "flawed" because it focussed on "the role of this single nutrient, when obesity is caused by excess calories from any nutrient".
Gavin Partington, of the British Soft Drinks Association, said his industry had been "singled out" by the "punitive" tax of sugary drinks.
He called for more "holistic" policy on obesity which did not "pick on one category".
FGDP(UK) Dean, Dr Mick Horton, responded:
“Eating and drinking too much sugar can cause tooth decay, obesity, type-2 diabetes, heart disease, stroke and even cancer, yet as a nation we consume a third more than we did 25 years ago and almost three times the recommended amount. A single can of cola contains more than a child’s reference intake of sugar for an entire day, so is it any surprise that two in ten children in England are obese by the time they leave primary school, or that tooth extraction is the primary reason why children are admitted to hospital?
“While we’re pleased to see the commitment to the Sugar Levy, in not restricting advertising and price promotions, nor investing in providing dietary and preventative oral health advice, the government has missed a golden opportunity to empower the public to make healthier choices and tackle the rise in avoidable dental extractions.”
Professor Nigel Hunt, Dean of the Faculty of Dental Surgery, said:
“We have continually drawn attention to the impact sugar has on children’s oral health. While we welcome the proposed sugar tax as a big step forward, although the revenue it raises could be used to fund more oral health programmes, the lack of ambition outlined in this Government document leaves a sour taste in the mouth of dentists who have fought hard for tougher measures. The average five year old child eats their own weight in sugar each year so it is crystal clear that much more needs to be done. We will continue to push new ministers hard on further action to protect the nation’s oral health.”