The fragile truce between India and Pakistan appeared to be largely holding on its first full day after some initial skirmishing, as both countries turned on Sunday to making the case that they had come out on top in the four-day conflict.

President Trump announced on Saturday that the two sides had agreed to a cease-fire with the help of U.S. mediation. That brought a halt to a military confrontation that had involved drones, missiles and intense shelling, and that had escalated, with strikes on military bases in both countries.

Mr. Trump followed up with a congratulatory note on Sunday, praising the two sides for “having the strength, wisdom, and fortitude to fully know and understand that it was time to stop the current aggression that could have lead to to the death and destruction of so many, and so much.”

He added that he would increase trade “substantially” with both countries, and that he would work with them to see if a “solution can be arrived at” to settle their seven-decade dispute over the Kashmir region.

Pakistan, a onetime close ally of the United States that has faded in importance, praised the American role as a mediator. But in India, the Trump administration’s public descriptions of its role in the mediation seemed to touch some sensitive spots politically.

The Indian government has long framed its relations with Pakistan as a strictly bilateral matter, and in the hours after the cease-fire was announced, India said it had been negotiated directly between Indian and Pakistani officials.