(Adds staff union protest, paragraphs 12-13) By Evelyn Leopold UNITED NATIONS, Oct 3 (Reuters) - U.N. Secretary-General Ban Ki-moon will soon discuss new steps to address human rights violations in Myanmar, where the military government is cracking down on protesters, with Security Council members. The secretary-general said on Wednesday he would meet his special envoy, Ibrahim Gambari, who recently spent four days in Myanmar, on Thursday and they would report to the 15 council members in a private meeting on Friday. "I am going to do whatever I can to, first of all, address this issue, the overall human rights situation in Myanmar," Ban told reporters. "That is one of the top concerns of the international community." "We will discuss closely with the Security Council members (how) to take action in the future," he said. Ban said he was "relatively relieved" that Gambari was able to meet government leaders as well as Aung San Suu Kyi, the opposition leader who has been under house arrest 12 of the last 18 years. Myanmar's military rulers told Gambari he could visit again next month. Meanwhile, they are continuing their crackdown against suspected protesters. In one house near the Shwedagon Pagoda in Yangon, the holiest shrine in the Buddhist nation and a focal point of last week's monk-led marches, only a 13-year-old girl remained after he parents were seized in the middle of the night. Among those arrested was a local U.N. staff member, two of her family members and her driver. Mynt Ngwe Mon, 38, a program assistant for the U.N. Development Program, was picked up from her house at 4 a.m. local time along with her husband, Than Tun, and brother-in-law Aung Kyaw Sint, a U.N. official said. Her driver was seized later at the same house. Asked about the arrests, Ban said, 'I am going to do whatever I can." The United Nations has appealed to Myanmar's U.N. mission, saying Mynt Ngwe Mon was on medication. Charles Petrie, the senior U.N. official and humanitarian coordinator in Yangon, sent a similar letter to Myanmar government officials. The U.N. Staff Union said Myanmar was in violation of U.N. General Assembly resolutions that call on countries "to provide adequate and prompt information" in the event of an arrest of U.N. personnel and allow independent medical teams to visit. The union's security committee, in a statement, called "this violation of the security and independence of U.N. staff unacceptable." Ban also pointed to a strong statement against Myanmar issued by the Association of Southeast Asian Nations and said he met with ASEAN ministers as well as Myanmar's Foreign Minister Nyan Win during this week's General Assembly session. "I again made it quite clear that it is the collective political responsibility of ASEAN, and I am going to take it as a high priority issue," Ban said. The Security Council will meet in closed session despite a U.S. request for an open meeting due to Chinese objections, diplomats said.