The two countries are taking advantage of a period when Earth and Mars are favourably aligned for a short journey, with the US spacecraft due to lift off on July 30.
It is a crowded field. The United Arab Emirates launched a probe on Monday that will orbit Mars once it reaches the Red Planet.
But the race to watch is between the United States and China, which has worked furiously to try and match Washington's supremacy in space.
The Chinese mission is named Tianwen-1 ("Questions to Heaven") in a nod to a classical poem that has verses about the cosmos.
It launched on a Long March 5 -- China's biggest space rocket -- from the southern island of Hainan.
Chinese authorities have yet to confirm the success of the launch.
Tianwen-1 is expected to arrive in February 2021 after a seven-month, 55-million-kilometre (34-million-mile) voyage.
The mission includes a Mars orbiter, a lander and a rover that will study the planet's soil.
"As a first try for China, I don't expect it to do anything significant beyond what the US has already done," said Jonathan McDowell, an astronomer at the Harvard-Smithsonian Center for Astrophysics.
The United States has already sent four rovers to Mars since the late 1990s.
The next one, Perseverance, is an SUV-sized vehicle that will look for signs of ancient microbial life, and gather rock and soil samples with the goal of bringing them back to Earth on another mission in 2031.
The Chinese mission is similar to NASA's Viking missions in 1975-1976, in that it has both an orbiter and a lander, McDowell said.
Tianwen-1 is "broadly comparable to Viking in its scope and ambition", he added.