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."
Rueda, who previously coached Colombia in the qualifiers for the 2006 World Cup, took over at the start of 2007.
In three years he rebuilt and united the Honduras squad and led them to the World Cup finals for the first time since 1982.
"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.
Rueda said he had received an offer to coach Ecuador, which he was considering, and one to coach the United Arab Emirates, which was less attractive.
"It's a different culture, a lot of money but it means sacrificing my family, sacrificing myself professionally," he said.
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