The T2T-CHM13 complete human reference genome contains ∼200 Mb of newly resolved sequence, improving read mapping and variant calling compared to GRCh38. However, the benefits of using complete reference genomes in other contexts are unclear. Here, we present a reference T2T-CHM13 recombination map and phased haplotype panel derived from 3202 samples from the 1000 Genomes Project (1KGP). Using published long-read based assemblies as a reference-neutral ground truth, we compared our T2T-CHM13 1KGP panel to the previously released GRCh38 1KGP phased callset. We find that alignment to T2T-CHM13 resulted in 38% fewer assembly-discordant genotypes and 16% fewer switch errors. The largest gains in panel accuracy are observed on chromosome X and in the regions flanking disease-causing CNVs. Simons Genome Diversity Project samples were more accurately imputed when using the T2T-CHM13 panel. Our study demonstrates that use of a T2T-native phased haplotype panel improves statistical phasing and imputation for samples from diverse human populations.