ABSTRACT Recent studies suggest that ultra-short-period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of Kepler planets: USPs have smaller radii (1–1.4R⊕) and larger mutual inclinations with neighbouring planets than nominal Kepler planets, and their period distribution is steeper than longer period planets. We study a ‘low-eccentricity’ migration scenario for the formation of USPs, in which a low-mass planet with initial period of a few days maintains a small but finite eccentricity due to secular forcings from exterior companion planets, and experiences orbital decay due to tidal dissipation. USP formation in this scenario requires that the initial multiplanet system have modest eccentricities (≳0.1) or angular momentum deficit. During the orbital decay of the innermost planet, the system can encounter several apsidal and nodal precession resonances that significantly enhance eccentricity excitation and increase the mutual inclination between the inner planets. We develop an approximate method based on eccentricity and inclination eigenmodes to efficiently evolve a large number of multiplanet systems over Gyr time-scales in the presence of rapid (as short as ∼100 yr) secular planet–planet interactions and other short-range forces. Through a population synthesis calculation, we demonstrate that the ‘low-e migration’ mechanism can naturally produce USPs from the large population of Kepler multis under a variety of conditions, with little fine-tuning of parameters. This mechanism favours smaller inner planets with more massive and eccentric companion planets, and the resulting USPs have properties that are consistent with observations.