With process technology scaling, accurate gate-level timing analysis becomes even more challenging. Highly resistive on-chip interconnects have an ever-increasing impact on timing, signals no longer resemble smooth saturated ramps, while gate-interconnect interdependencies are stronger. Moreover, efficiency is a serious concern since repeatedly invoking a signoff tool during incremental optimization of modern VLSI circuits has become a major bottleneck. In this paper, we introduce a novel machine learning approach for timing estimation of gate-level stages using current source models and the concept of multiple slew and effective capacitance values. First, we exploit a fast iterative algorithm for initial stage timing estimation and feature extraction, and then we employ four artificial neural networks to correlate the initial delay and slew estimates for both the driver and interconnect with golden SPICE results. Contrary to prior works, our method uses fewer and more accurate features to represent the stage, leading to more efficient models. Experimental evaluation on driver-interconnect stages implemented in 7 nm FinFET technology indicates that our method leads to 0.99% (0.90 ps) and 2.54% (2.59 ps) mean error against SPICE for stage delay and slew, respectively. Furthermore, it has a small memory footprint (1.27 MB) and performs 35× faster than a commercial signoff tool. Thus, it may be integrated into timing-driven optimization steps to provide signoff accuracy and expedite timing closure.