TOKYO, Aug 24 (Reuters) - Japan will waive pre-departure COVID-19 tests for vaccinated travellers to the country, but daily caps on entrants will remain in place, Prime Minister Fumio Kishida said on Wednesday.

Japan has maintained some of the strictest pandemic border measures among major economies, requiring travellers to present a negative coronavirus test taken within 72 hours of departure.

"From Sept. 7, we will no longer require people who have been vaccinated three times to present proof that they are not infected," said Kishida, who addressed reporters online as he is recuperating from COVID at his official residence.

Domestic and foreign business groups have urged a greater relaxation of Japan's border controls, saying the measures risk inflicting further economic pain.

Kishida said in May that he wanted to bring Japan's border measures more in line with those of other Group of Seven nations.

Japan in June opened up to tourists for the first time in two years, but requirements that they apply for visas and stick to guided, package tours have kept actual numbers of inbound visitors small.

Local media reported on Tuesday that Japan may raise a daily cap on inbound travellers from 20,000 to 50,000, but no decision has been made, Kishida said.

"We will continue relaxing these measures gradually," he said. "We hope to announce something soon based on the quarantine setup and the situation with infections."

The border easing comes as Japan deals with a seventh wave of infections, driven by the infectious BA.4 and BA.5 variants, that have forced companies to idle production lines and driven COVID deaths to a record 343 on Tuesday.

All the same, Kishida is pushing a living "with corona" strategy of weathering the surge without imposing restrictions on businesses or mobility, and focusing medical resources on elderly and high-risk patients.