De novo assembly enables investigations of unknown genomes, paving the way for personalized medicine and disease management. However, it faces immense computational challenges arising from the excessive data volumes and algorithmic complexity. While state-of-the-art de novo assemblers utilize distributed systems for extreme-scale genome assembly, they demand substantial computational and memory resources. They also fail to address the inherent challenges of de novo assembly, including a large memory footprint, memory-bound behavior, and irregular data patterns stemming from complex, interdependent data structures. Given these challenges, de novo assembly merits a custom hardware solution, though existing approaches have not fully addressed the limitations. We propose NMP-PaK, a hardware-software co-design that accelerates scalable de novo genome assembly through near-memory processing (NMP). Our channel-level NMP architecture addresses memory bottlenecks while providing sufficient scratchpad space for processing elements. Customized processing elements maximize parallelism while efficiently handling large data structures that are both dynamic and interdependent. Software optimizations include customized batch processing to reduce the memory footprint and hybrid CPU-NMP processing to address hardware underutilization caused by irregular data patterns. NMP-PaK conducts the same genome assembly while incurring a 14X smaller memory footprint compared to the state-of-the-art de novo assembly. Moreover, NMP-PaK delivers a 16X performance improvement over the CPU baseline, with a 2.4X reduction in memory operations. Consequently, NMP-PaK achieves 8.3X greater throughput than state-of-the-art de novo assembly under the same resource constraints, showcasing its superior computational efficiency.