The Chief District Office (CDO) in Kathmandu, a powerful civilian body in charge of all security issues in the Kathmandu valley, last week summoned the editors after they left blank spaces on the pages where they normally publish editorial comment, the lawyer said on Wednesday.
The king - who sacked the coalition government, assumed absolute power and declared emergency rule on 1 February - issued a proclamation prohibiting for six months "any interview, article, news, notice, view or personal opinion" against his actions.
Those to present themselves on Wednesday are Gopal Budhathoki, editor of the weekly Sanghu (Bridge), and the editors of three other weeklies.
Budhathoki is also vice-president of the Federation of Nepalese Journalists (FNJ).
Six journalists have been detained since the king's takeover, including FNJ general-secretary Bishnu Nisthuri.
The International Federation of Journalists at the weekend demanded the release of the six, an end to press censorship and the restoration of democracy in the Himalayan kingdom.
The president of the Brussels-based federation, Christopher Warren, said the group "found unacceptable the repression of journalists' rights to freedom of expression". The Indian and British governments said on Tuesday they had frozen military aid to Nepal after the king failed to reverse his seizure of power.