The April 16 letter said that while ETA is now consigned to history, the drive for Basque independence would continue.
The decision, ETA said in the letter, "doesn't overcome the conflict that the Basque Country maintains with Spain and with France".
In recent months a dozen of the 51 ETA members being held in France have been moved closer to their families, with more planned in the future. We must not repeat mistakes; we must not let problems fester.
It wasn't immediately clear why the letter was dated two weeks earlier. The official, who wasn't authorised to be named in media reports, declined to elaborate.
The Basque militant group ETA is announcing that it has "completely dissolved all its structures", in a letter sent to Basque institutions and civil society groups.
Zoido assured that there would be no "impunity" and "before and after this communique, they will be pursued wherever they are in order to be arrested".
"ETA obtained nothing through its promise to stop killing, and it will obtain nothing by announcing what they call dissolution", he said. In 1973, it killed Luis Carrero Blanco, Gen Franco's prime minister, with a auto bomb. The Spanish government fears that ETA members and sympathizers could score political points with a negotiated surrender.
The group - deemed a "terrorist organisation" by several countries including Spain, France, and the United States - was founded in 1959 during General Francisco Franco's rule in Spain. ETA also injured more than 2,600 people, kidnapped 86 and threatened hundreds more, according to the latest government count.
Critics charge that Basque pro-independence parties like Sortu, which include among its ranks people once part of or linked to ETA, are trying to impose their own version of events, while separatists argue that Basques have been repressed for decades, even centuries, by Spain and France.