HAVANA - Rene Gonzalez, one of the so-called "Cuban Five" spies convicted of conspiracy and espionage in the United States, is renouncing his US citizenship so that he can permanently remain in Cuba.

Gonzalez went to the US Interest Section in Havana on Monday to begin the process, accompanied by his lawyer Phillip Horowitz, the official Prensa Latina news agency reported.

Gonzalez, 56, who was born in Chicago and has a wife and two children in Havana, said he felt happy to be with his family. Gonzalez has been in Cuba since April 22 to attend a memorial service for his father.

Gonzalez was released from a US prison in October 2011 after being jailed for 13 years, and has since been serving a three-year probation.

The US Justice Department had insisted that Gonzalez complete his probation in the United States, but recently reversed its position.

US District Judge Joan Lenard, in charge of the case since 2001, accepted Gonzalez's proposal to fulfil the rest of his probation in Cuba if he renounced his US citizenship.

Gonzalez was arrested in 1998 along with his compatriots and members of the "Wasp Network" -- Geraldo Hernandez, Ramon Labanino, Antonio Guerrero and Fernando Gonzalez. The five were accused of spying on US military installations in southern Florida, Cuban exile groups and politicians opposed to the Cuban government.

The four others remain jailed in the US prison and also have to serve probation when released.

Insisting the five men did not threaten US national security, Cuba said they were only monitoring opposition activists who reportedly were planning a violent overthrow of the Cuban government.

Besides the "Cuban Five," another thorny issues of US- Cuba relations is the case of US contractor Alan Gross, who is serving a 15-year jail term in Cuba for illegally installing Internet service for Cuban Jewish groups.

Cuban officials have hinted at a possible swap of the "Cuban Five" for Gross, but Washington has rejected the idea.