India marked its Republic Day on Saturday with a veiled warning to Pakistan that its hand of friendship should "not be taken for granted" after deadly border clashes between the two sides.

Celebrations were being held under heavy security, especially in New Delhi where large areas were sealed off for an annual parade of military hardware at which Bhutan's king Jigme Khesar Namgyel Wangchuck was chief guest.

India's President Pranab Mukherjee told rival Pakistan in his annual address to the nation on the eve of the celebrations that New Delhi's hand of friendship should "not be taken for granted".

His warning came amid a ceasefire which took hold last week in the disputed region of Kashmir after the nuclear-armed nations agreed to halt cross-border firing that has threatened to unravel a fragile peace process.

"We believe in peace on the border and are always ready to offer a hand in the hope of friendship... but this hand should not be taken for granted," he said.

Before the ceasefire, Pakistan said three of its soldiers died in firing by Indian troops along a de facto border dividing Kashmir between the two nations.

India, in turn, accused Pakistani troops of killing two of its soldiers, one of whom was beheaded, and the Himalayan region remains on edge.

India and Pakistan have fought three wars since partition in 1947, two of them over Kashmir that both claim.

Snipers manned rooftops along the route of the parade in New Delhi while helicopters monitored the area from above.

Tens of thousands of security forces were deployed across the capital and around the country for Republic Day -- a holiday celebrated in all parts of India as the day when the nation's constitution took effect.

In his speech, the president also said it was time for India to "reset its moral compass" following the savage gang-rape and murder of a student last month that ignited nationwide demonstrations to press for better safety for women.

Mukherjee said the death of the 23-year-old woman, "who was a symbol of all that new India strives to be", had shattered the nation's complacency.

"We lost more than a valuable life -- we lost a dream" and "we must look deep into our conscience and find out where we have faltered", he said.