Russian news reports said that eight people had been killed in the incident, although these figures have yet to be confirmed by authorities.
The Chinese government said three Chinese crew members were rescued after the sinking while seven others are missing.
"We hope they continue with the search and rescue operations for the missing sailors and clarify the reason [for the incident] as soon as possible," Jiang said.
The Russian coast guard has confirmed it opened fire on the cargo ship before it sank - saying it had left the Pacific-coast port of Nakhodka without permission, and then refused to stop.
The vessel was held at the port earlier this month, suspected of involvement in smuggling, officials said.
According to Russia's Kommersant business daily, Russian border guards blamed the captain of the Chinese ship for the possible deaths of the sailors.
"[He] did not take all necessary measures to fight for the survivability of his ship," the paper quoted an official as saying.
Kommersant said the crew of the Chinese ship included 10 Chinese nationals and
six Indonesians, including the captain.
In video footage of the incident broadcast on Russian television, gunfire could be heard.
"The captain was called by radio, border guard boats sent light signals, a special flag demanding to stop was raised and a warning shot was fired," Alexander Selentsov, a prosecutor in Nakhodka, told the Interfax news agency.
Interfax also quoted a border guard captain as saying the Chinese ship " disregarded authorities' demands and was fleeing to the Chinese economic zone at full speed".
Andrei Samarkin, a chief investigator familiar with the case, told Kommersant that Russian border guards had fired "several hundred shots" from a 30mm automatic cannon in the direction of the ship after it refused to stop following "numerous light and sound signals".
He said eight sailors, including the ship's captain, were rescued from a closed raft about 30 minutes after the ship sank and taken aboard a Russian patrol vessel.
Eight other sailors on an open raft were likely doomed, he added.
"Due to extremely severe weather conditions, there was no chance whatsoever of helping those on an open raft," Samarkin said.
"These sailors did not wear wetsuits, and when they were washed off into the sea they quickly received lethal hypothermia."