The two vessels, also carrying six helicopters, left the western port of Kure and are scheduled to arrive in the Philippines on Friday, said a defence ministry spokesman.
He added that Japan's Self-Defense Forces (SDF) are sending a total of 10 planes today to the disaster-struck nation -- seven C-130 transport planes, two KC-767 tanker planes and one U-4 multi-purpose support aircraft.
The troops' duties will include providing medical support and transporting relief goods.
An advance team of about 50 SDF personnel was sent last week while the total troop deployment was expected to rise to almost 1,200 in all.
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It is the first time Japanese troops have been active in Leyte -- an area hit hard by Super Typhoon Haiyan -- since the island turned into one of the biggest battlegrounds of World War II when US forces counter-invaded in 1944.
The 1,180-strong contingent will be the largest single relief operation team ever sent abroad by Japan's defence forces.
Previous overseas missions by the SDF, which adheres to the country's post-war pacifist constitution, have usually numbered in the hundreds.
The previous record was 925 personnel sent in 2005 to Sumatra after the Indonesian island was ravaged by a massive earthquake-triggered tsunami.