New UN High Commissioner for Human Rights Michelle Bachelet on Wednesday regretted Washington's withdrawal from the UN Human Rights Council.

"I do believe it is very important that all member states are engaged in this universal battle for human rights," she told reporters when asked to comment on the U.S. withdrawal.

Every country has the right to decide if they participate or not in a UN entity, she said. "But I would believe it would be good for the world that every member of the United Nations is engaged in this big battle for human rights and humanity."

In the past, the United States had been a strong supporter of human rights, of the UN Office of the High Commissioner for Human Rights, which she now leads, said Bachelet.

The United States announced its withdrawal from the Geneva-based UN Human Rights Council in June, becoming the first member to quit.

Iceland was elected in July into the council to take the seat of the United States.

The UN Human Rights Council has 47 members, which are elected at the UN General Assembly for staggered three-year terms on a regional group basis.