"Differences are permissible in all positions except in the governance position," al-Rai al-Aam said in a front-page editorial on Saturday.
"Personal judgments are needed in every aspect with the exception of the (ruling) family issue. Political manoeuvres are tolerated in every field, but not in the field of decision-making," it said.
The appeal comes a week after Shaikh Salim al-Ali al-Sabah, who heads the National Guard and is ranked fourth in the family hierarchy, made his second statement in as many months for the family to unite, reform and avoid differences and disputes.
"The regime is a red line," al-Rai al-Aam said. "We urge the family to exert an exceptional effort to put an end to the black ideas ... and black practices," it added, without elaborating.
The daily also said the family had to set an example to others.
The Kuwaiti press, which enjoys considerable freedom, has in the past few months highlighted the affairs of the ruling family in light of the health situation of the amir and crown prince.
The 76-year-old amir, Shaikh Jabir al-Ahmad al-Sabah, who has been at the helm for 27 years, suffered a minor brain haemorrhage in 2001.
Discord within the ruling family is
a staple of Kuwait's media fare
Although he has since carried out most of his official duties, he opened parliament last month looking frail and requiring assistance coming in and out of the gallery.
The 73-year-old crown prince, Shaikh Saad al-Abd Allah al-Sabah, who is now seldom seen in public, underwent colon surgery in 1997 and has since been undergoing treatment.
Gulf diplomats said two months ago that Kuwait was preparing to name the country's prime minister, Shaikh Sabah al-Ahmad al-Sabah, who is also the amir's half-brother, as the new crown prince.
The changes were expected to be announced at a meeting of the ruling family that was scheduled for late September, but diplomatic sources said the meeting and the changes were postponed due to a lack of consensus in the family.