Himmat Singh, the chief of India's Border Security Force (BSF) in Punjab, confirmed that his troops had responded to the rocket fire early on Saturday.
"We retaliated with machine-gun fire," he said.
Raza said: "When the rockets were fired, they fired on the Pakistani side.
"It was light firing from their side and we lodged a protest ... it was unprovoked.
"We did not retaliate as it's the international border and the situation could have escalated."
Singh said it was not clear who had launched the rockets into Indian territory, but that they had been fired from the Pakistani side of the border.
"We have lodged a protest with the Pakistan Rangers and are trying to ascertain who is responsible for the rocket attacks," he said.
A Punjab village councillor accused Pakistani soldiers of trying to intimidate an all-female paramilitary contingent, which was the first to be deployed at the Wagah border.
"Firing from Pakistan is a vicious attempt to demoralise the village folks as well as newly deployed lady soldiers," Baljit Singh said.
The Wagah crossing is popular with tourists who travel there to watch a ceremonial military change of Pakistani and Indian guards at sunset.
The Indian military said this was the first such incident in the area.
Exchanges of gunfire along the so-called Line of Control dividing the region of Kashmir, over which the two neighbours have fought two of their three wars, have continued occasionally since a ceasefire deal in 2003.
But, despite tense relations - most recently over the attack on the Indian city of Mumbai earlier last November - confrontations almost never take place along the agreed border between the nuclear-armed states.
New Delhi has blamed a Pakistan-based group for the attack on Mumbai, which left more than 160 people dead, and accused "official agencies" of supporting the assailants.
Islamabad has repeatedly dismissed the claims.