In a statement, the Ministry of External Affairs also said New Delhi continues to monitor the situation closely.
"We are concerned at the deteriorating security situation along the Blue Line. We continue to monitor the situation closely," the MEA said.
The 120-km Blue Line is a United Nations-recognised demarcation line to indicate that Israel had withdrawn its military from southern Lebanon. It separates Lebanon from Israel and the Golan Heights, but it is not an official international border.
"Inviolability of UN premises must be respected by all, and appropriate measures taken to ensure the safety of UN peacekeepers and the sanctity of their mandate," the MEA said in its statement.
The United Nations Interim Force in Lebanon (UNIFIL), the UN peacekeeping mission in Lebanon, said in a statement on October 10 that "recent escalation along the Blue Line is causing widespread destruction of towns and villages in south Lebanon".
"In the past days, we have seen incursions from Israel into Lebanon in Naqoura and other areas. Israel Defense Forces (IDF) soldiers have clashed with Hizbullah elements on the ground in Lebanon," it alleged in the statement.