The two landslides occurred in separate parts of Dafang county, the first at around 3 am (1900 GMT Wednesday) and another at 9 am, state broadcaster CCTV said.
"Preliminary investigations (showed)... that 19 people were trapped" in the debris, it said.
Aerial footage by the broadcaster showed a village inundated by brown mud that blanketed farming fields and pooled at the foot of a densely forested mountain.
The emergency management ministry said it urged rescue teams to make "every possible effort" to recover the missing people.
But it said the remote region was "high and steep" and that rescue efforts were proving "difficult".
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