Any city or village may, without petition or creating a street improvement district, grade, curb, gutter, and pave any portion of a street otherwise paved so as to make one continuous paved street, but the portion to be so improved shall not exceed two blocks, including intersections, or thirteen hundred and twenty-five feet, whichever is the lesser. Such city or village may also grade, curb, gutter, and pave any unpaved street or alley which intersects a paved street for a distance of not to exceed one block on either side of such paved street. The improvements authorized by this section may be performed upon any portion of a street or any unpaved street or alley not previously improved to meet or exceed the minimum standards for pavement set by the city or village for its paved streets.