In a series of Twitter posts addressed directly to Mr Maduro, Mr Almagro also called him a "petty dictator".
Mr Maduro accused the OAS chief earlier this week of being a CIA agent and a traitor himself.
The Venezuelan president has blamed his country's economic crisis on an axis of enemy forces co-ordinated from the US.
During a three-hour long news conference on Tuesday, Mr Maduro had justified his declaration of a state of emergency by saying Venezuela was under attack from imperialist forces led by the CIA.
He then told journalists: "Almagro, just give up. He has been a traitor for a long time... At some point I will tell his story, I know his secrets. The Americans, the CIA, have played a master move using Almagro as their agent."
Mr Almagro, who before leading the OAS was the foreign minister of his native Uruguay, had already clashed with Mr Maduro last year after he called him "rubbish".
Mr Almagro had responded on that occasion with an eight-page open letter, saying he would be "rubbish" if he ignored the plight of the Venezuelan people.
His Twitter posts this week were both more concise and more direct.
Linking to his open letter to Mr Maduro, Mr Almagro said: @NicolasMaduro I'm not a traitor either to my ideas or my principles BUT YOU ARE A TRAITOR to your people.
In a series of 12 tweets, he also told the Venezuelan president that "you will NEVER be able to undo so much suffering, intimidation, misery and anguish you've created for your people".
He also said Mr Maduro would "NEVER be able to bring back to life the children who've died because of lack of medicine".
Venezuelan doctors say a shortage of essential medicine has reached a crisis point.
Mr Almagro also urged Mr Maduro to allow a recall referendum to go ahead.
Opposition politicians have handed in a petition with 1.85 million signatures to the electoral authorities requesting a referendum be held to recall Mr Maduro from office.
But Mr Maduro's deputy, Vice-President Aristobulo Isturiz, on Sunday ruled out such a referendum, saying the signatures were "fraudulent".
Mr Almagro said that not letting the referendum go ahead made Mr Maduro "another petty dictator".
While President Maduro did not answer Mr Almagro's tweets directly, Venezuelan Foreign Minister Delcy Rodriguez did.
She wrote, "Mr Almagro, every time you make a statement you express your hatred against Venezuela and its legitimate authorities. You are part of the imperialist detritus."
"You only repeat the scripted words which your imperialist masters dictate to you".
"You will never give orders to Venezuela!"
The former president of Uruguay, Jose Mujica, has also commented on the row between Mr Almagro, who served as Mr Mujica's foreign minister, and President Maduro.
Asked what he made of the bitter exchange, he said using a popular Spanish saying that Mr Maduro was "crazy as a goat".
"They're all crazy in Venezuela, they call each other all sorts of things but they're not going to fix anything this way."
While Mr Mujica is known for his direct and outspoken manner his words are damaging to Mr Maduro, who has always praised the former left-wing president as a "comrade".
The head of the Organization of American States (OAS), Luis Almagro, has accused the Venezuelan President Nicolas Maduro of being "a traitor".