DHAKA, July 19 (Reuters) - Bangladesh has lodged a formal protest with India over the shooting dead of two border guards earlier in the week, a foreign ministry statement said on Saturday.

Bangladesh said on Friday that two Bangladeshi troops and an Indian border guard were killed in an exchange of fire on Thursday. But the Indian embassy in Dhaka said in a statement that one of its Border Security Forces (BSF) guards was injured in the incident.

"In a strong protest Bangladesh said the incursion and firing on Bangladesh troops were totally unacceptable and hoped that the Indian authorities will take appropriate action against those responsible and ensure that such incidents do not recur," the statement said.

The India High Commission in Dhaka rejected the allegation of an incursion on Saturday.

"The BSF pursued some cattle smugglers travelling in boats in Indian territory," it said in a statement. "The smugglers fired at BSF upon which BSF retaliated. During this exchange of fire, one BSF constable sustained serious bullet injuries."

Despite generally friendly relations between the two countries, Indian and Bangladeshi border guards often exchange fire along their 4,000-km (2,500-mile) porous border, which runs through the rice fields, hills, jungles, marshes and rivers.

In 2001, at least 16 Indian and three Bangladeshi solders were killed in the deadliest border clash between the two countries. (Reporting by Masud Karim, Writing by Nizam Ahmed; Editing by Alex Richardson)

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