Holmes, who arrived here on Saturday for a three-day visit, was to meet with Human Rights and Disaster Management Minister Mahinda Samarasinghe.
"The top priority remains the preservation of the lives of the tens of thousands of civilians still trapped inside the combat zone," Holmes said in a statement at the start of his mission.
"I also want to see the people in the camps, to visit UN staff being held there, and to review how the sudden outflow of so many people from the combat zone is being managed.
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The UN says dozens of its local Tamil staff are being held in government-run camps for internally displaced people. The Sri Lankan government has resisted all calls to halt an offensive that is now on the brink of wiping out the Tamil Tiger rebels, who have been fighting for an independent Tamil homeland since 1972.