(Corrects headline to read 60th anniversary, not 50th)

By Simon Denyer

NEW DELHI, Aug 15 (Reuters) - Indian Prime Minister Manmohan Singh, speaking on the 60th anniversary of independence from British rule, said the country needed to work harder to fight poverty, ignorance and disease despite fast economic growth.

"India cannot become a nation with islands of high growth and vast areas untouched by development, where the benefits of growth accrue only to a few," he said on Wednesday from the ramparts of New Delhi's historic Red Fort behind a bulletproof glass screen.

"We have moved forward in the many battles against poverty, ignorance and disease. But can we say we have won the war?"

India is one of the world's fastest growing economies, but has some of the sharpest inequalities in the world, with hundreds of millions of poor surviving on a fraction of a dollar a day.

Sharpshooters were stationed on nearby buildings as Singh spoke, while troops and armed police guarded roads and key buildings around the country on a day traditionally marked by violent attacks by separatist militants or Maoist rebels.

Earlier, Singh laid wreaths at memorials commemorating the leader of India's freedom movement Mahatma Gandhi, as well as its first Prime Minister Jawaharlal Nehru and his daughter, assassinated former Prime Minister Indira Gandhi.

The prime minister, dressed in his trademark light blue turban, then proceeded to the Mughal-era fort where he unfurled the national flag to a 21-gun salute.

"NATIONAL SHAME"

Singh promised to invest in agriculture, which still employs more than half of India's population, and in education, in a country where a third of the population remains illiterate.

He also vowed renewed efforts to promote industrialisation and build "first-rate infrastructure".

"The problem of malnutrition is a national shame," he added. "I appeal to the nation to resolve and work hard to eradicate malnutrition within five years."

Despite growth rates of around eight percent in recent years, around 46 percent of children under three are undernourished, UNICEF says, a higher rate than in sub-Saharan Africa.

"We are a young nation," he said. "Once unleashed, the energy of our youth will drive India onto a new growth path."

"However we must not be overconfident. We have a long march ahead. We need at least a decade of hard work and of sustained growth to realise our dreams."

Security has been dramatically stepped up around the country for the Independence Day holiday, with police monitoring traffic entering Delhi and the financial centre of Mumbai, both of which have been frequently targeted by militants.

Far away in India's remote northeast, separatists in the oil- and tea-rich state of Assam have already killed 30 people in the past week, including women and children, all of them Hindi-speaking settlers.

The United Liberation Front of Asom has been fighting for independence since 1979 and accuses New Delhi and non-Assamese people of plundering Assam's resources and ruining its culture.

In Kashmir, scene of a violent 17-year insurgency against Indian rule, separatist groups have called for a general strike, calling the anniversary a "black day" and the celebrations "meaningless" until Kashmir got freedom.

Ordinary life has also been been disrupted in the run-up to the anniversary by a security crackdown, with unpopular "cordon and search" operations and frisking of civilians stepped up.

Singh said a special effort was needed to bring prosperity to less developed regions like Kashmir and the northeast.

In eastern India, Maoist insurgents have distributed leaflets in towns and villages asking people to boycott the celebrations.

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