After rising to within 17 points of the 20,000 mark, the Dow was up by just 15 points at 19,870 at 11:36 a.m. ET. The S&P 500 was down 5 points (0.24%), while the Nasdaq was down 21 points (0.4%).
Biotech stocks were particularly whacked after Trump took aim at the pharmaceutical industry, saying it had become "disastrous."
Shares of the aerospace company Lockheed Martin also fell after Trump mentioned the firm. He had criticized costs of its F-35 Lightning II project.
The Dow rose to an intraday high of 19,999.63 last week Friday and tried several times but failed to cross 20,000.
CNN reported on Tuesday that Trump and President Barack Obama received classified briefing materials that showed Russian operatives claimed to have compromising personal and financial information on the president-elect.