The president-elect also repeated claims that Panama is "ripping us off".
On Sunday, Trump told a crowd of conservative activists: "The fees being charged by Panama are ridiculous, highly unfair."
If shipping rates are not lowered, Trump said, "we will demand that the Panama Canal be returned to us, in full, quickly and without question".
Trump has also said he did not want the Panama Canal "falling into the wrong hands" and specifically cited China.
China is the second-largest user of the Panama Canal after the US, according to data, and also has major investments in the central American country.
On Christmas Day, Trump fired off dozens of messages defending his policies and nominations, and repeated suggestions that the US annex Greenland and Canada.
It is unclear how serious Trump is about the territorial moves, or how they would be accomplished.
Up to 14,000 ships travel through the 51-mile (82km) canal each year, including container ships carrying cars, natural gas and other goods, and military vessels.
The canal was built in the early 1900s. The US maintained control over the canal zone until 1977, when treaties gradually ceded the land back to Panama. After a period of joint control, Panama took sole control in 1999.
Canal transit costs have increased over the past year due to a historic drought, according to shipping industry website Lloyd's List.
A Hong Kong-based company, CK Hutchison Holdings, manages two ports at the canal's entrances.