Aims. We aim at deriving stellar atmospheric parameters based on the photometric data from the Javalambre Photometric Local Universe Survey (J-PLUS) in addition to near-infrared photometry from the Two Micron All-Sky Survey (2MASS). Methods. Our method consists of a semi-supervised machine learning approach based on the k-means method combined with a modified K-nearest neighbors algorithm. This method compares the observed photometry to a set of reference data to estimate the stellar effective temperature (Teff), surface gravity (log g), and metallicity ([Fe/H]) of stars from J-PLUS Data Release 3 (DR3). For that, a set of 105 colors was constructed using extinction-corrected photometric data from J-PLUS DR3 and 2MASS. The reference dataset used was composed by the MESA Isochrones & Stellar Tracks (MIST) models, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), and the Apache Point Observatory Galactic Evolution Experiment (APOGEE) surveys. Results. We estimate Teff, log g, and [Fe/H], for approximately 5.6 million stars from J-PLUS DR3, along with their errors. Our results were in agreement with the spectroscopic estimates of LAMOST and APOGEE. We also applied a dimension reduction method, seeking greater efficiency by reducing the computation time and minimizing the information needed to calculate the stellar parameters, resulting in a subset of 11 colors. From this approach, stellar parameters were obtained for approximately six million stars, increasing the number of studied objects. The results obtained were of the same order, despite having slightly higher uncertainties compared to those obtained with 105 colors. Conclusions. Our results demonstrate the potential of using a method built from machine learning algorithms that does not require prior training. Additionally, we show that the proposed method allows the estimation of reliable atmospheric parameters even when the available photometry did not fulfill all the photometric quality criteria. As part of our method, we define a neighborhood parameter, which assesses the reliability of our estimates and indicates that objects with smaller neighborhood values have lower uncertainties.