(CNN) -- A well-publicized estimate that Typhoon Haiyan killed 10,000 people in the Philippines is "too much," and the death toll likely is closer to 2,000 or 2,500, President Benigno Aquino III told CNN's Christiane Amanpour on Tuesday.

Read: Typhoon Haiyan leaves 1,774 dead, aid efforts mobilize

"We're hoping to be able to contact something like 29 municipalities left wherein we still have to establish their numbers, especially for the missing, but so far 2,000, about 2,500, is the number we are working on as far as deaths are concerned," he said.

The monster storm left behind a catastrophic scene after it made landfall on six Philippine islands last Friday, leaving many without access to food and medical care. At least 800,000 people have been displaced, the United Nations said Tuesday.

By Tuesday, Philippines officials said 1,774 bodies had been counted and 2,487 people were injured.

The previous estimate of 10,000 killed, Aquino said, came from local officials who perhaps were "too close" to the center of destruction to make an accurate guess.

Read: Typhoon Haiyan crushed town 'like giant hand from the sky'

The typhoon simply overwhelmed the ability of two or three local governments to do their jobs, which include taking care of the initial response, the President said. For example, in Tacloban, only 20 of 290 police were available when disaster struck; many were tending to their own families, he said.

The national government "had to replace a lot of the personnel with personnel from other regions to take care of government's vital functions," Aquino said.

The typhoon wreaked havoc on power lines and communications facilities, which meant government officials faced immense difficulties in identifying needs and dispatching relief supplies and equipment. But the situation has improved, he said. All of the national roads are reopened and most of the airports are nearly back to normal operating levels, he said.

Still, he added, the sheer number of people affected is daunting.

Aquino said the toll might have been higher had it not been for preemptive evacuations, the prepositioning of supplies and cooperation from businesses. "But, of course, nobody imagined the magnitude that this super typhoon brought on us," he said.

Aquino expressed gratitude for the aid that has been pouring in from around the world. "There are, at last count, over 22 countries have either pledged to us, actually given us aid," he said.

Though civil order has broken down in some areas, some 2,000 personnel have been deployed to restore it, he said.

"People were -- became -- desperate, and that's why we are trying to fast-track the situation where national government takes over these local government functions so that order is restored."

Responding to a question about the vulnerability of his country to climate change, Aquino said he had no doubt that climate change is occurring and the world must respond to it. "There should be no debate that this is happening," he said, citing heavy rains during what used to be dry months, periods of drought during what used to be wet months and the havoc that that has inflicted on farmers.

"We all live on one planet," the President said. "Either we come up with a solution that everybody adheres to and cooperates with, or let us be prepared to meet disasters."

Efforts are under way to better prepare the archipelago nation to endure future such assaults, such as planting mangroves in tidal areas as a defense against tsunamis, and investing in meteorology to better predict -- and prepare for -- such events.

After the immediate needs of the populace are met, the nation's focus will turn to rebuilding the tens of thousands of homes affected -- this time to standards better able to withstand typhoons, Aquino said.