After New Delhi and Islamabad said they had shot down each other's warplanes in a dramatic intensification of a standoff triggered by a suicide attack on the Indian-controlled part of Kashmir earlier this month, Mogherini warned of the dangers of further escalation.

"This has the potential to lead to serious and dangerous consequences for the two countries and the wider region," she said in a statement.

"We expect both countries to now exercise utmost restraint and avoid any further escalation of the situation," she added, urging the two sides to resume diplomatic contacts to defuse the crisis.

Earlier, Pakistani Prime Minister Imran Khan called for talks, warning of potentially catastrophic consequences should "better sense" not prevail.

While both sides have sought to play down the threat of war, the rare aerial engagement over the divided and disputed Himalayan territory of Kashmir significantly raises the stakes between arch-rivals who have fought three wars since independence from Britain in 1947.

Pakistan says it has downed two Indian jets and taken one pilot into custody, while New Delhi confirmed the loss of one of its planes and said it had shot down a Pakistani fighter jet.