We describe a scatter and randoms weighted (SRW) iterative PET reconstruction algorithm. The SRW method is based on the estimation of the trues fraction (TF) within the prompts. Once the TF is estimated, it is then incorporated into the weighting component of the system matrix, and the net result is a scatter and randoms weighting in the sensitivity image similar to the attenuation correction weighting. Although using the measured prompts in the TF estimation was demonstrated to achieve the fastest convergence at high statistics, it is not reliable at low counts situations due to the sparse and noisy nature of the measured prompts. Therefore, a mean estimation of the prompts derived from the forward-projection of the reconstructed prompts image was introduced into the TF estimation. A contrast phantom was scanned and the data were reconstructed using the standard and the SRW methods. The contrast vs noise, precision vs accuracy in contrast, absolute error vs number of iterations comparisons, and standard deviation image over different realizations of the same object were evaluated at low counts situations, and it was observed that the SRW method outperforms the standard approaches such as the scatter and randoms data pre-correction and the Ordinary Poisson methods. The image intensity (activity) outside the object can also be minimized using the SRW method. In addition, further improvement in accuracy, precision, convergence, and noise properties can be achieved by further improving the TF and the prompts estimate.