President Ma Ying-jeou said hundreds of people were likely to have died.
He was visiting the rescue operation centre in Qishan in rural southern Taiwan.
Military helicopters have been ferrying villagers out of communities cut off by the storms and floods after roads and bridges were washed away.
"We have found around 700 people alive in three villages last night and 26 more this morning. We are deploying 25 helicopters to evacuate them," said Maj Gen Richard Hu, a senior official in the rescue effort.
The typhoon struck Taiwan at the weekend, causing the worst flooding in 50 years. The official death toll stands at 63.
'Save my village'
The BBC's Cindy Sui in Qishan says the authorities fear that hundreds more people could still be trapped.
In Hsiaolin alone, rescue workers said about 100 were unaccounted for as of Tuesday and thought possibly to have been buried alive.
Our correspondent says family members from surrounding areas have been converging on Hsiaolin, demanding that helicopters be sent to their villages too.
Some are carrying signs that read, "Save my village".
The search for survivors has been a slow process as the only way in and out of the villages is by helicopter, our correspondent adds.
The BBC's Alastair Leithead, also at the Qishan rescue base, says a high school playing field has become a landing pad for helicopters, and ambulances are lining the running track to ferry the injured to hospital.
Alastair Leithead: "It's been another tough day for the rescuers"
Morakot lashed Taiwan with at least two metres (80in) of rain over the weekend.
It is typhoon season in the North West Pacific, which brings storms like Morakot with exceptionally high rainfall and strong winds, said Liam Dutton from the BBC Weather Centre.
But, to put it in context, he said Morokot brought around 40 times as much rain to Taiwan as would fall on a typical wet weekend in the United Kingdom.
Typhoon Morakot has caused at least $225m (£135m) in agricultural damage, while nearly 30,000 houses are still without power and 750,000 homes are without water, according to the latest estimates from officials.
The storm also hit mainland China, where about 1.4 million people were evacuated from coastal areas, eight people died in flooding and up to 10,000 homes were destroyed.
In the town of Pengxi in China's eastern province of Zhejiang, a landslide toppled seven older houses, reportedly killing two people.
Meanwhile in Japan, another seasonal storm, Typhoon Etau, caused floods and landslides that have killed at least 15 people since the weekend and left a dozen missing.
About 1,000 people spent Tuesday night in shelters and 4,600 households were without water, officials said.
TAIWAN FLOODED BY TYPHOON MORAKOT
1. Rainfall recorded in Alishan, Taiwan between 7-9 August 2009
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.