Besides the mounting tensions and artillery fire along the border areas between the two countries the department said terrorists are operating in the region who previously have attacked Americans.
"Tensions between India and Pakistan have risen to serious levels, and the risk of intensified military hostilities cannot be ruled out," the warning said.
Terrorist groups, some of which are linked to al Qaida, "are active there as well and have attacked and killed civilians," some of them Americans.
"The Department of State urges American citizens who remain in India to consider departing the country," the department statement said, with the same advice to Americans in Pakistan.
Although the U.S. embassy and consulates in Pakistan will remain available, however, from "time to time" they may temperarily suspend operations "to review their security posture."
In India, Americans should register and obtain updated security information from the Embassy or nearest Consulate, the warning said.
"Events in the Middle East also increase the possibility of violence," the Department said.
In Pakistan, as security is increased at official U.S. facilities, "terrorists and their sympathizers will seek less well-protected targets," the department warned. "These may include facilities where Americans are generally known to congregate or visit, such as clubs, restaurants, places of worship, schools or outdoor recreation events."