"If the Filipino government fails to respond in a positive manner within 72 hours, the hiring of Philippine workers will be frozen," presidential office spokeswoman Lee Chia-fei warned.
Hung Shih-cheng, the skipper of the 15-tonne "Kuang Ta Hsin No 28", was killed during the incident, which also left the boat riddled with more than 50 bullet holes.
"This is nothing but a slaughter," prosecutor Liu Chia-kai told reporters after examining the ship.
Taiwan's government has come under pressure from the opposition and the media to take action, with the Philippines refusing to apologize and saying the coastguard was tackling illegal fishing.
Philippine coastguard spokesman Commander Armand Balilo said Friday the incident took place in Philippine waters and the crew had been carrying out their duties to stop illegal fishing.
"If somebody died, they deserve our sympathy but not an apology," Balilo told reporters.
The victim's son, who was with his father and two other sailors on the boat when the shooting took place, has insisted they did not cross into Philippine waters.
In Manila, Abigail Valte, a spokeswoman for Philippine President Benigno Aquino, told a government radio station Saturday that authorities had launched a "transparent and impartial investigation" into the incident. The coastguard crew involved in the incident had been temporarily suspended to ensure a fair probe.