NEW DELHI — Prime Minister Imran Khan of Pakistan announced on Thursday that his country would be releasing a captured pilot from India after days of military conflict, offering a way out of the crisis and seeking to position Pakistan as the cooler head in a confrontation that has put the world on edge.

“In our desire of peace, I announce that tomorrow, and as a first step to open negotiations, Pakistan will be releasing the Indian Air Force officer in our custody,” Mr. Khan said.

After hours of relative lull throughout Thursday, the gesture appeared to be a face-saving opening for both countries to head off a war. But Indian officials were guarded, saying that the pilot’s release would not necessarily end the crisis, which they said was rooted in Pakistan’s support of terrorist groups that strike at India.

The days before had brought both nations to the brink. On Tuesday, Indian warplanes dropped bombs inside Pakistan — it is not clear what they hit — and Pakistan shot down at least one Indian fighter jet on Wednesday. Tens of thousands of troops have been rushed to the countries’ border, heavy artillery barrages and gunfire have been volleyed across it, and tank columns have been chugging into place for what many feared could turn into a full-blown war.

Both nations wield nuclear weapons, and China, the United States, Britain and many other countries have been urging them to step away from conflict, which began after a suicide bomber killed more than 40 Indian paramilitary troops in the disputed region of Kashmir on Feb. 14. India accuses Pakistan of aiding in the attack, which was claimed by the terrorist group Jaish-e-Mohammed, but Pakistan has denied it.

At a news conference after his summit meeting in Vietnam on Thursday, President Trump said that there was “reasonably decent” news coming from India and Pakistan and “hopefully it’s going to be coming to an end.”

From the beginning of the showdown, Pakistan’s military publicity wing has demonstrated a knack for dominating the narrative. In particular, the almost immediate official circulation of videos that appeared to show the Indian pilot being first protected from a mob by Pakistani forces, and then remarking on how well he was being treated (“The tea is fantastic!” he said in one clip), became a virally blooming propaganda coup on social media.

But on Thursday, Indian officials insisted that was part of the problem — and made a point of noting that displaying prisoners for propaganda purposes violates the Geneva Conventions.

They suggested that Mr. Khan’s move was an empty ploy that ignored the real problem between the two countries. A senior Indian official told reporters in New Delhi that even if the captured pilot were returned home, there would be no chance “to go back to zero” and ease tensions unless Pakistan acted against terrorist groups that it has traditionally used as proxies against India