Jan 17 (Reuters) - The Baltic Exchange"s dry bulk sea freight index (.BADI) fell for a seventh straight session on Monday as rates declined across all its vessel segments. * The overall index, which factors in rates for capesize, panamax and supramax vessels, slipped 33 points, or 1.9%, to 1,731 for its lowest since early last March. * The capesize index (.BACI) fell 26 points, or 1.7%, to 1,470, its lowest since late February. * Average daily earnings for capesize vessels, which transport 150,000-tonne cargoes such as iron ore and coal, dropped by $217 to $12,190. * Benchmark Dalian and Singapore iron ore futures fell on Monday, dragged down by improving near-term supply of the steelmaking ingredient and signs of continuing economic weakness in top steel producer China. * The panamax index (.BPNI) dipped 49 points, or 2.1%, to 2,326. * Average daily earnings for panamax vessels, which ferry 60,000-70,000 tonne coal or grain cargoes, fell by $441 to $20,935. * The supramax index (.BSIS) fell 33 points to its lowest level since April at 1,864.