Heavy rain hit mountainous Sichuan province near the epicentre of the quake, where survivors are still living in tents and pre-fabricated houses.
At least 80,000 people were killed in the May 12 earthquake.
"So far, we have moved 18,000 residents who were threatened with danger to safe areas. We are now relocating the other 2,000," a government spokesman was quoted as saying by the official Xinhua news agency.
The rain and landslides have also damaged more than 40,000 houses and flattened another 16,000, the report added, as well as killed more than 5,000 head of cattle.
The downpours began to pound Mianyang city and the surrounding countryside on Monday night.
Mianyang encompasses Beichuan and other areas that were the hardest-hit counties in the Sichuan earthquake.
(Reporting by Ben Blanchard; Editing by Valerie Lee)
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