Rueda took Honduras to just their second World Cup in South Africa where they were lost to Chile and Spain and drew with Switzerland without managing to score a goal.
"Since the World Cup, the pillars of union, respect and credibility have started to weaken," said Rueda, adding that the problems began with criticism of the squad he picked for the tournament.
"If we had followed the same route we would have got better results, but after we qualified a lot of factors came together and these prevented us from producing a better performance."
"The atmosphere is not the best, so we've decided to step aside," the Colombian told a news conference, referring to himself and his coaching staff.
"I'd like to repay the friendship and generosity that the country has shown to myself and especially my family," added Rueda, who broke down in tears at the end of the conference.
"It's a different culture, a lot of money but it means sacrificing my family, sacrificing myself professionally," he said.
