The United States, European Union, China, and Russia have expressed growing concerns that the worst crisis in years between bitter nuclear rivals India and Pakistan could spiral out of control.

The Pentagon on February 27 said Acting Defense Secretary Patrick Shanahan is focused "on de-escalating tensions and urging both of the nations to avoid further military action."

EU foreign policy chief Federica Mogherini said India and Pakistan should show the "utmost restraint."

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

China, a close ally of Pakistan, expressed "deep concern" over the escalation of violence and expressed hope that Islamabad and New Delhi will "earnestly fulfill their commitments to preventing the expansion of the situation."

Russia also urged calm and offered to act as a mediator.

Tensions have soared between the two countries, mainly centering on the disputed Himalayan region of Kashmir.

Pakistan and India on February 27 said they had shot down each other's warplanes near the border separating their portions of Kashmir.

The Pakistani military said its air force had downed two India Air Force jet in its airspace and captured a pilot on the ground in the Pakistan-controlled part of Kashmir.

India confirmed the loss of one of its fighter jets and said a pilot was missing while it foiled an attack by Pakistan jets over the Himalayan region. It also said it had shot down a Pakistani jet, which Islamabad has denied.

The aerial dogfight came after a night of artillery attacks by both sides across the Line of Contact (LoC), the de-facto border that separates Kashmir.

An Indian defense force spokesman said Pakistan used heavy-caliber weapons at several sites along the LoC.

"The Indian Army retaliated for effect and our focused fire resulted in severe destruction to five posts and number of casualties," the spokesman said.

The recent troubles surfaced on February 14, when a Pakistan-based terror group claimed responsibility for a suicide attack that killed at least 41 Indian troops in Muslim-majority Kashmir.

In response, India sent its warplanes to carry out an air strike in northeastern Pakistan on what New Delhi said was a training camp used by the Jaish-e Mohammad (JeM), the militant group that claimed responsibility for the February 14 attack.

A senior Indian government source said 300 militants were killed in the strike. Pakistan says no one died.

Trump on February 22 said prior to the Indian air strike that it was a "very dangerous situation between the two countries. We would like to see it stop."

He added that "India is looking at something very strong. India just lost almost 50 people with an attack. So I can understand that also."

Pakistan's envoy to the United States, Asad Majeed Khan, on February 27 said Washington’s failure to condemn the Indians’ strike inside Pakistani territory is "construed and understood as an endorsement of the Indian position, and that is what emboldened them even more.”

U.S. Secretary of State Mike Pompeo on February 27 said he spoke separately with the foreign ministers of both countries and urged them to avoid "further military activity."

"I expressed to both ministers that we encourage India and Pakistan to exercise restraint, and avoid escalation at any cost," Pompeo said in a statement.

"I also encouraged both ministers to prioritize direct communication and avoid further military activity," he said.

Nuclear-armed India and Pakistan have fought two of their three full-fledged wars over Kashmir since their partition during independence from Britain in 1947.

With reporting by Reuters and AFP