"There are developments in the case, but to protect the secrecy of the investigation we prefer not to provide any details," prosecution spokesman Sofiene Sliti told AFP.
However, Interior Minister Mohamed Ali Aroui said "more than 10 people have been arrested for direct or indirect involvement in the attack, among them people who provided logistical support".
He declined to say whether they included nine people already reported arrested, including the father, sister and two brothers of one of the gunmen police killed in the attack, Jabeur Khachnaoui.
On Wednesday, the two gunmen targeted tourists visiting the National Bardo Museum, killing 21 people, including a policeman.
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The dead tourists were four Italians, three Japanese, three French, two Spaniards, a Colombian, an Australian-Colombian, a British woman, a Belgian woman, three Poles and a Russian.
Dr Chadli Dziri, chief of surgery at the Charles Nicolle hospital in Tunis, said that of 43 people wounded there were still concerns about the prognosis for one, a Frenchwoman shot in the stomach and the leg.
On Thursday, the Islamic State group claimed it was behind the attack and threatened more.
Authorities said the gunmen had trained in neighbouring Libya, where the IS is believed to have training camps.
Tunisia has seen an upsurge in Islamist extremism since the 2011 revolution that ousted dictator Zine El Abidine Ben Ali and sparked the Arab Spring.
Tunisia has taken pride in forming a democratic government and achieving stability since the Arab Spring in marked contrast to countries such as Egypt and Libya.