The Yi Peng Three left the Russian port of Ust-Luga, west of St Petersburg, on 15 November.
Early on 17 November, the Arelion cable between the Swedish island of Gotland and Lithuania was damaged.
The following day, the C-Lion 1 cable between the Finnish capital Helsinki and the German port of Rostock was severed.
Data from ship tracking websites suggest the Yi Peng Three sailed over the cables at around the time that each was cut.
According to the Wall Street Journal, investigators suspect the ship deliberately damaged the cables by dropping and dragging its anchor along the seabed for more than 160km (100 miles).
The ship has been in the Kattegat strait - a passage between Sweden and Denmark that connects the Baltic Sea to the North Sea - since 19 November and is being monitored by the Danish navy.
On Thursday, Swedish Prime Minister Ulf Kristersson told a press conference that his government had "sent a formal request to China to co-operate with Swedish authorities in order to create clarity on what has happened".
"We think it's extremely important to find out exactly what happened and, of course, we expect also China to comply with the request we have sent," he said.
He also reiterated an earlier request for the ship to move back into Swedish waters so it could be searched as part of the investigation, though added that he was not making an "accusation" of any sort.
In response on Friday, China's foreign ministry said it is "willing to work with related countries to find out the truth".
"Currently China and Sweden maintain close communication regarding this," spokeswoman Mao Ning said.
The period since Russia's full-fledged invasion of Ukraine in February 2022 has seen heightened tension in the Baltic Sea and a number of incidents involving damage to undersea infrastructure.
In September 2022, a series of explosions blew holes in the two Nord Stream gas pipelines between western Europe and Russia, and in October 2023 damage was done to an undersea telecoms cable between Estonia and Sweden.
Speaking last week, German Defence Minister Boris Pistorius said of the latest incident that "nobody believes that these cables were cut accidentally", though he did not specify who he believed was responsible.
Russia has rejected suggestions it could have been involved as "absurd" and "laughable".