National interest as a concept has various meanings. 

One classic definition says it is the interests of a nation as a whole held to be an independent entity separate from the interests of smaller groups and other nations.

Another definition renders national interest as those basic core values, such as national security and free exercise of sovereign powers, which a nation cherishes and strives to preserve at any cost. 

National interest reserves the rights that guarantee the survival of a nation. Usually national interest is prioritized with all others' interests being secondary.  It is a basis for foreign policy. 

Further, national interest cannot be decreed in statutes; it's a sixth sense and it evolves with a nation's history, with national experience.

Public interest, on the other hand, is the interests of a collective of citizens - independent of state institutions. It's a kind of collective civil interest.

The dichotomy between national interest and public interest does not mean that the two are contradictory, nor does it mean that the state is necessarily anti-people or that the people are necessarily anti-state. 

National interest and public interest, as claimed, should not be confused with the self-interest of individuals.  To illustrate: we may agree it's in the national interest to expose corruption in government; but at a given moment, a government representative may argue to a journalist that a given exposé should at least be delayed "in the national interest". But this would be the government's or the ruling party's immediate self-interest, to protect its image; not the national interest as such.

Many economists in government have the simple view of policy in the national interest as being any policy which contributes to national income and growth. The view that government should seek the happiness of the greatest number. 

There will be those who do not accept the national interest - it's their right. But don't let them claim to speak on our behalf; don't let them hold us back.