He likened the region to a patient that has been moved out of the emergency room into an intensive care unit.
"We have overcome the most difficult part," he said. "In the first week we can say we were in the emergency room ... this second week we are now in the ICU, still critical but stabilized."
He said the hard-hit Leyte provincial capital of Tacloban reported 1,725 dead. "I believe this number in Tacloban city is not yet final," he said.
Most of the bodies have been buried in mass graves, many of them unidentified, he said.
"It is possible that some of the missing are among the unidentified," he said.
Journalists in Tacloban say the stench of death from piles of debris, upturned vehicles and remnants of what once were homes indicates that bodies remain trapped underneath.
Roxas said the situation was stabilizing, with major roads on Samar and Leyte cleared of debris and some banks, grocery stores and gas stations now open.
More troops and police have been brought to the region from other parts of the country to beef up law and order.
The airport in Tacloban, the regional hub, and its seaport are operating.
"There is no more looting," he said. "We are now heading to recovery and reconstruction."
Haiyan hit the eastern seaboard of the Philippines on Nov. 8 and quickly barreled across its central islands, packing winds of 235 kilometers (147 miles) per hour and gusts of up to 275 kph (170 mph), with a storm surge of 6 meters (20 feet).
Even though authorities evacuated about 800,000 people ahead of the typhoon, the death toll was high because many evacuation centers schools, churches and government buildings could not withstand the winds and water. Officials said people who sought shelter in the buildings drowned or were swept away.
The United States and about two dozen other governments quickly sent aid. Bottlenecks, including roads blocked by debris, damaged vehicles and a lack of personnel, held up the distribution of relief supplies in the first week.
U.S. Marines helped clear the Tacloban airport runway, allowing the delivery by air of aid to the city which became the relief center for the region.
Roxas said more than 1.1 million food packs have been delivered to the region.
"Our mission is to deliver relief and food supplies to all the towns ... (with) 100,000 food packs every day," he said.
Typically, a food pack consists of rice, noodles, canned goods and instant coffee sufficient for a family for two days.
The United Nations on Friday boosted its appeal for Philippines typhoon relief by nearly 16 percent from $301 million to $348 million with a further rise likely.
"A massive disaster like this requires a massive response," U.N. Humanitarian Coordinator Valerie Amos told reporters at the United Nations. "Much more needs to be done. Food, clean water and shelter remain the top priorities.
