Ma, who has faced heavy criticism from victims of the disaster, ruled out resignation, insisting his government did its best in the face of difficulties, however he pledged an investigation into any irregularities.
"Certainly, I will take full responsibility whatever the blame is because, after all, I am the president of this country," Ma told CNN, saying heavy rains grounded rescue helicopters in the first few days after the storm hit, delaying relief.
"Once the weather was good -- that is the 14th of August -- we were able to evacuate 2,518 people. It's a record," he said.
Hundreds of people still await rescue in remote areas of Taiwan, where torrential downpours, dense fog, rugged terrain and raging rivers have hampered relief efforts. Washed-out roads and collapsed bridges have made some rescue operations impossible.
Touring disaster areas, Ma has been confronted by angry survivors, and even provoked a scuffle when he opened a weekend baseball game as protesters demanded he step down.
Ma has refused to quit, instead offering apologies and promises to do better.
"We will find out not only to correct the mistakes but (also) to punish the people responsible," he said.
Rescue efforts were ongoing Sunday with military helicopters bringing stranded villagers to their waiting relatives.
Others, waiting days in anguish for word on their loved ones, lashed out in anger.
"Local officials don't care," one man said. "There are still people there and they don't do anything."
On Saturday, weeping relatives of typhoon victims set up shrines near devastated villages to calm the spirits of the dead and honor the belief that their souls will return home after seven days.
Morakot hit the island last weekend, dropping 2.6 meters (102 inches) of rain. Before it roared on to mainland China on Sunday, the storm killed at least 123 people in Taiwan.
The death toll could climb to more than 300 after more villagers buried by mudslides and floodwaters are found, Taiwan officials have said.
Southern and central Taiwan were hardest hit by the storm.
Mudslides inundated some places in the south, including the village of Shiao Lin, where 160 homes were lost. Authorities believe hundreds of people could be trapped under five stories of mud in the village.
International aid efforts were mobilizing on Sunday, however these were complicated by diplomatic pitfalls in the face of China's territorial claims over Taiwan, which it considers a renegade province.
The United States said Saturday it would send food, portable shelters and other aid items to Taiwan in the coming days.
In aiding Taiwan, the United States must be sensitive to its territorial relationship with China, the sources said.