Last week, Armenia, who won four of their World Cup qualifiers and managed a 2-2 draw with Italy, climbed to a best-ever 38th place in the FIFA rankings.
"We, of course, respect Vardan Minasyan's decision but we would like him to reconsider it," the players said in an open letter published on the Armenian football federation (FFA) website.
On Monday Minasyan, 39, said he had rejected a contract extension.
"At this moment, I prefer another way to continue my career as a coach," he said. "I have received a number of offers, mainly from abroad, and I plan to consider them."