The warning followed a string of deadly border clashes between the two sides in the disputed Kashmir region.
President Pranab Mukherjee’s warning comes amid a ceasefire which took hold last week in Kashmir after the Indian and Pakistani armies 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,” Mukherjee said in a televised address on the eve of the country’s Republic Day celebrations.
“But this hand should not be taken for granted,” he added.
Before the ceasefire, Pakistan said three of its soldiers had been killed in firing by Indian troops along a de facto border dividing Kashmir between the two nations that is known as the Line of Control.
India, in turn, accused Pakistani troops of killing two of its soldiers, one of whom was beheaded.
Pakistan has denied any responsibility for the violence.
“Neighbours may have disagreements, tension can be a subtext of frontiers,” Mukherjee said.
“But sponsorship of terrorism through non-state actors is a matter of deep concern to the entire nation.”
Mukherjee was referring to Indian suspicions that the Lashkar-e-Taiba militant group that India blames for the deadly 2008 Mumbai attacks in which 166 people died may have helped to instigate the hostilities.
Nuclear-armed India and Pakistan have fought three wars since partition in 1947, two of them over the Kashmir region that both nations claim.
A ceasefire, which is periodically violated by both sides, has been in place along the Line of Control since 2003.
Republic Day marks the date in 1950 when India’s new constitution came into effect.
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