India and Pakistan appeared to be dangerously escalating their armed confrontation on Thursday, as both countries said that their military sites had come under attack, and heavy shelling and strikes were reported overnight on each side of their border.

The military face-off began on Wednesday, when India struck several sites in Pakistani territory — its deepest strikes inside Pakistan in decades — in retaliation for a deadly terrorist attack two weeks before.

In a sign of the international alarm that the conflict could spin out of control, Secretary of State Marco Rubio spoke with leaders from both countries on Thursday and emphasized the need for “immediate de-escalation,” according to State Department accounts of the calls.

India and Pakistan both continued to claim that they were not seeking an escalation in their military clash. But the reality on the ground indicated that the two nuclear-armed countries were not yet ready to take the offramps from their boiling tensions that had appeared to take shape a day before.

The Indian government said on Thursday that it had thwarted Pakistani attempts to unleash drones and missiles at Indian military targets in more than a dozen cities and towns, many of them home to air force bases.

India said it had responded by striking Pakistan’s air defense systems and radars close to the city of Lahore — the kind of blow that often causes a military conflict to intensify, analysts said.

Subscribe to The Times to read as many articles as you like.