The presidents of Colombia and Mexico attended a formal ceremony in Mexico City, where Garcia Marquez lived for more than three decades.
Earlier, residents in his home town of Aracataca in Colombia’s Caribbean region held a symbolic funeral.
He was considered the finest writer of the Spanish language since Cervantes.
Garcia Marquez was cremated at a private family ceremony in Mexico City last week.
A funeral cortege took the urn containing his ashes from his house to the historic centre of the Mexican capital, where the memorial ceremony was held.
It was placed on the podium of the majestic Palace of Fine Arts, which is where Mexico pays tribute to its late artistic icons.
The ornate cultural venue was adorned with yellow flowers, the author’s favourite, and musicians also performed some of his favourite pieces.
Thousands of admirers filed past the urn, and joined the author’s wife, Mercedes Barcha, and sons, Rodrigo and Gonzalo, to say their goodbyes.
The event was also attended by Mexican President Enrique Pena Nieto and his Colombian counterpart Juan Manuel Santos.
“He was probably the greatest Colombian we have had in our history,” President Santos told the BBC’s Will Grant in an exclusive interview.
“The world knows about Colombia through Gabriel García Marquez. He represented what Colombia is in many ways. His magic realism is – and he said it – is not an invention. It’s a description of what Colombia is.”
Earlier, Colombia held a ceremony of its own in Garcia Marquez’s birthplace of Aracataca, the inspiration for Macondo, the setting for his 1967 seminal masterpiece One Hundred Years of Solitude, which sold millions of copies around the world.
A local resident Elvia Vizconte said the novelist would be remembered for generations to come.
“He was a very important person here in Aracataca. And now he leaves us a very special legacy for new generations, his novels, his tales, his stories,” she told the Associated Press news agency.
On Tuesday, the Colombian government will hold a formal ceremony at the main cathedral in the capital Bogota, an event which will be televised.
Then on Wednesday, Colombians will have readings of Garcia Marquez’s novel No One Writes to the Colonel in hundreds of libraries, parks and universities across the country.
The BBC’s Arturo Wallace in Bogota says there was some sadness in Colombia that the first main event to commemorate Garcia Marquez was taking place in Mexico rather than his country of origin.
But Colombians also understand that he made Mexico his home and, despite his frequent trips to Colombia, they were used to his absence, our correspondent adds.
The writer fled Colombia in 1981 after learning that the country’s military wanted to question him over links to left-wing guerrillas.
Fellow writers, politicians and cultural figures from around the world paid tribute to the author.
He achieved fame for pioneering magical realism, a unique blending of the marvellous and the mundane in a way that made the extraordinary seem routine.
With his books, he brought Latin America’s charm and teeming contradictions to life in the minds of millions of people.
By Will Grant