The investigation, which the new administration had promised after winning January elections, comes after the previous regime resisted a UN inquiry into claims that up to 40,000 ethnic Tamil civilians were killed under Rajapakse's command in the final months of a war that ended in May 2009.
Foreign Minister Mangala Samaraweera will travel to Geneva next month to meet UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein, the foreign ministry said in a statement.
"Minister Samaraweera wants to brief the Human Rights Council about the new steps that Sri Lanka wishes to take," an official said, asking not to be named.
"Sri Lanka is looking for about two months to establish a new (domestic) mechanism."
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The government has pledged a credible, independent investigation that may draw on foreign expertise and experience.
Last week, the UN postponed the publication of an eagerly-awaited report on a UN-mandated war crimes probe into Sri Lanka's brutal separatist war, giving the new government time to prove its bona fides.
Samaraweera's talks with Zeid come after the government secured parliamentary approval Thursday for a long-awaited witness protection law, a key demand of the international community to ensure accountability in the island.
The new government has also pledged to enact a right to information law, another demand of both local and international rights activists who accused the previous regime of persecuting and silencing critics and dissidents.
Former strongman Rajapakse, who ruled the country for a decade, had insisted that not a single civilian was killed while crushing Tamil rebels and refused to cooperate with any foreign probe, a move that drew international censure.