SRINAGAR, India — Separatist leaders called for a shutdown in Indian-controlled Kashmir on Saturday as Indian Prime Minister Narendra Modi paid a daylong visit to review development work and inaugurate road projects.

The visit came a day after rivals India and Pakistan shelled each other’s security posts and villages, killing four civilians on each side and an Indian soldier.

Shops, businesses and schools were shut while thousands of paramilitary troops and police in flak jackets spread out across Kashmir and closed off roads with razor wire and iron barricades in anticipation of anti-India protests and clashes.

Separatist groups that challenge India’s sovereignty over Kashmir called for the strike as well as a march to the commercial hub in the main city of Srinagar to protest Mr. Modi’s visit.