He also told security authorities on Saturday to end a week-long protest outside the presidential office by supporters of his narrowly defeated opponent.
"It has been a week, isn't that enough?" Chen told his first news conference since his re-election last Saturday. "I have demanded relevant agencies to restore social order before next week. This has to be cleared up, we can't tolerate this any more."
He ordered the protesters to disperse by Monday.
"If I am unable to handle those crowds in front of the office, then I will not be qualified as a national leader," he said. "I'm still the president.
"Our tolerance is limited. Our tolerance must not be taken for granted," he told reporters at the presidential office.
Chen won last Saturday's direct presidential election, only the island's third, by 30,000 votes out of more than 13 million cast and by the narrowest margin in a Taiwan presidential.
Thousands continue to protest in
front of the presidential office
But Nationalist party leader Lien Chan and his running mate have raised doubts about the shooting in which Chen was lightly wounded in the abdomen by an unidentified sniper on the eve of last Saturday's election and have called for an independent investigation.
"If they can create the same kind of wound, A-Bian will immediately resign from the presidency, I will not be sworn in on 20 May and if they want a new election they can have a new election," Chen told his first news conference since he won last Saturday's presidential election by just 30,000 votes out of more than 13 million cast.
"If you can't do it or you are afraid of doing it, then shut up," he told them.
Earlier in the day, defeated Nationalist party leader Lien Chan led half a million supporters outside Chen's office in Taiwan's biggest ever political protest to dispute the narrow election result and to demand a recount.