TOKYO, Sept 4 (Reuters) - Outgoing Prime Minister Yoshihide Suga will back the popular minister in charge of Japan"s vaccination rollout, Taro Kono, for the Liberal Democratic Party"s (LDP) leadership race this month, broadcaster Nippon News Network reported on Saturday. The leader of the ruling party will replace Suga as prime minister. Suga announced on Friday that he would not run in a party leadership contest slated for Sept. 29, meaning he will also be replaced as prime minister. read more Suga, who is expected to stay on until his successor is chosen in the party election, had a medical checkup on Saturday but there was nothing wrong with his health, the Kyodo news agency said, citing unidentified people around him. Hours after Suga"s announcement, broadcaster TBS reported, without citing sources, that Kono intended to run in the leadership race. But Kono stopped short of declaring his candidacy, telling reporters that he wanted to consult party colleagues first. A former foreign and defence minister, Kono, 58, is popular among young voters after building support through Twitter, where he has 2.3 million followers - a rarity in Japanese politics, which is dominated by older men less adept with social media. Former foreign minister Fumio Kishida has already thrown his hat in the ring, while several others have voiced interest in running in the race. Kishida said on Saturday he would leave a national sales tax at its 10% rate if elected as premier, reiterating that he would fund a new economic package worth tens of trillion yen by issuing more government bonds. "I"m not thinking of touching the sales tax for the time being," Kishida told a Nippon News Network programme. "We then must consider Japan"s finances from the standpoint of how to make use of the fruit of economic growth." Japan had six prime ministers in as many years before Suga"s predecessor, Shinzo Abe"s record eight-year tenure.