June 3 (Reuters) - The Baltic Exchange's dry bulk sea freight index, which tracks rates for ships carrying dry bulk commodities, rose for a fifth straight session on Tuesday on firmer rates for capesize and panamax vessel segments.

* The main index .BADI, which monitors rates for capesize, panamax and supramax shipping vessels, was up 8 points, or 0.6%, at 1,430 - its highest since April 4.

* The capesize index .BACI gained 33 points, or 1.4%, to 2,333, its highest since April 3.

* Average daily earnings for capesize vessels .BATCA, which typically transport 150,000-ton cargoes such as iron ore and coal, added $279 to $19,350.

* Iron ore futures fell to their lowest in nearly two months due to demand fears sparked by U.S. President Donald Trump's plan to double tariffs on steel imports and on weak factory data in top consumer China. IRONORE/

* The panamax index .BPNI gained 1 point, or 0.1%, to 1,108, breaking an eight-session losing streak.

* Average daily earnings for panamax vessels .BPWT, which usually carry 60,000-70,000 tons of coal or grain, rose $6 to $9,973.

* "We see the capesize sector paving the way, with iron ore exports from Brazil and Australia to China increasing," said Yiannis Parganas, head of Intermodal's research department.

"Given the wide premium of capesize rates over panamax, some cargoes are now being split and shifted toward panamax vessels as well."

* Among smaller vessels, the supramax index .BSIS lost 6 points, to 942 points, its lowest since April 15.

* On the trade policy front, the Trump administration is urging countries to submit their best trade offers, ahead of a five-week deadline, according to a draft letter seen by Reuters.

(Reporting by Ishaan Arora in Bengaluru; Editing by Maju Samuel)

((Ishaan.Arora@thomsonreuters.com;))