Nine people have been arrested in connection with Wednesday's gun attack in Tunis that left 23 people dead, including 20 foreign tourists, the Tunisian presidency says.
It alleged that four were directly linked to the attack and five had "ties to the cell".
The army will also be deployed to major cities, the presidency added.
In another development, Islamic State said in an audio message that it was behind the attack.
It said the attack was carried out by "two knights of the caliphate" and named them as Abu-Zakariya al-Tunisi and Abu-Anas al-Tunisi.
A statement described the attack as a "blessed invasion of one of the dens of infidels and vice in Muslim Tunisia".
The statement was published by Twitter accounts known to be reliable sources of IS propaganda.
One of two gunmen involved in the Bardo museum attack, named by Tunisian officials as Yassine Laabidi, was reportedly known to the authorities.
Laabidi and his accomplice, named as Hatem Khachnaoui, were killed as security forces stormed the museum.
It was not immediately clear how the identities of the gunmen corresponded to the names given by IS. Jihadist groups, including IS, often give their fighters noms de guerre.
Tourists from Japan, Colombia, the UK and other European countries were killed in the attack and more than 40 people were injured.
The suspects arrested on Thursday were not identified and no further details of their alleged involvement were given.
However, BBC security correspondent Frank Gardner says an al-Qaeda operative has claimed that the two gunmen had spent two months training with Islamist militants in Derna, eastern Libya, before slipping back into Tunisia.
In a statement, the presidency said Tunisia was facing "exceptional circumstances", adding that "terrorist operations have now moved from the mountains to the cities".
"After a meeting with the armed forces, the president has decided large cities will be secured by the army," the statement added.