TOKYO, April 8 (Reuters) - Hong Kong-based activist investor Oasis Management said on Monday it owns more than 3% of Japanese cosmetics and skincare firm Kao, in its latest announcement after last week revealing its efforts to promote change at the company.

Oasis, which has been pressuring Kao to streamline its brand portfolio, has been investing in the company for over four years and actively engaging with the company for the last nine months, the fund's founder and chief investment officer, Seth Fischer, told a press conference in Tokyo.

Oasis launched a campaign against Kao on Thursday last week, calling on Kao to prioritise its international marketing and streamline its "bloated brand portfolio" as it has lost market share to competitors in recent years.

Fischer said that Kao has no board members with international marketing experience and called for both the appointment of a chief marketing officer and for more diversity on the board, adding that the cosmetics maker had only one female board member, down from two a year ago.

Oasis' stake gives it full shareholder rights and Fischer said Oasis was considering all available options, including calling for an annual general meeting and submitting shareholder proposals.

Fischer said that he had tried multiple times to meet with Kao President Yoshihiro Hasebe but was not offered a meeting until May. He said Oasis went public with their concerns as they were unsatisfied by Kao's response to their private engagement.

"Their existing brands have such growth potential," Fischer said. "They have the right products, they simply need to focus on marketing." (Reporting by Anton Bridge and Makiko Yamazaki; Editing by Tom Hogue and Christopher Cushing)