Nov 23 (Reuters) - The Baltic Exchange"s dry bulk sea freight index rose for a fourth straight session on Tuesday to its highest level in a week as rates rose across its vessel segments. * The overall index (.BADI), which factors in rates for capesize, panamax and supramax vessels, gained 70 points, or 2.7%, to 2,715 points. * The capesize index (.BACI) rose 171 points, or 4.4%, to 4,055, its highest in more than three weeks. * Average daily earnings for capesizes, which transport 150,000-tonne cargoes such as iron ore and coal, rose $1,421 to $33,631. * China"s benchmark iron ore futures surged on Tuesday as steelmakers were set to resume production after rigorous controls in the past few months following government orders. * The panamax index (.BPNI) increased 42 points, or 1.8%, to 2,333. * Average daily earnings for panamaxes, which ferry 60,000-70,000 tonne coal or grain cargoes, increased by $380 to $21,000. * The supramax index (.BSIS) added 8 points to 2,243, snapping a four-session losing streak. Reporting by Kavya Guduru in Bengaluru; Editing by Aditya Soni