Peralta, 26, was shot in a shopping mall parking lot in La Ceiba, but no suspects have been identified.
"We won't rest until those responsible for this act are identified and detained so that they can face justice," the government said.
Authorities did not say what day Peralta was killed and have ruled out robbery as a motive, since Peralta's belongings were not taken from him.
The 26-year-old played as a midfielder for the Honduras national team and for C.D. Olimpia
, a club based in Honduras' capital, Tegucigalpa.
Among his former club teams was Scotland's Rangers F.C., which he left in January
after arriving in the summer of 2013.
The Glasgow club said it would observe a minute of silence for Peralta before its home match Saturday against Greenock Morton F.C.
Honduras has topped the list for the world's highest murder rate in recent years, the U.N. Office on Drugs and Crime has said.
International teammate Boniek Garcia -- who plays for Houston Dynamo in MLS -- was one of the first to pay tribute.
"Rest in peace brother, God will receive you in heaven, you will stay in our hearts. Strength to the family," he tweeted.
His club Olimpia also paid its respects.
"We deeply regret the death of our player Arnolt Peralta. The Olimpia family is in mourning," it said on the club's Twitter page.
MLS side Seattle Sounders was another club to pay its condolences.
"Our thoughts go out to Olimpia and the friends and family of Arnold Peralta," they said.
Another international teammate, and former Premier League star, Hendry Thomas paid tribute.
"What sad news. Rest in peace Arnold."