A senior government official said some of the bodies were found stuck in the waterbed, while others were floating.
The passenger bus had rammed the railing of a bridge and plunged into Gogra canal at Balirghat area of the district around 6 am yesterday.
The search operation was called off last night due to poor visibility and resumed at 7 am this morning, Murshidabad District Magistrate P Ulaganathan told PTI.
"The search will continue till the time we are convinced that there are no bodies stuck anywhere underneath the water," he said.
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"We have so far managed to identify 39 persons. The bodies of the six unidentified persons are kept in the morgue of Murshidabad Medical College and Hospital. We have been receiving calls from relatives of passengers" he said adding those rescued are undergoing treatment at the hospital.
"The district magistrate and senior police officers, including the SP, are monitoring the situation," Ulaganathan said.
Asked about eye witnesses' claims that the bus driver was talking over phone and speeding, the DM said, "It is still not clear what the reason was. But there was fog in the morning and visibility was poor. We are investigating the matter".
"Forensic experts will check whether there was any problem with the engine of the bus," he said.
Expressing grief over the accident, West Bengal Governor K N Tripathi today urged people to join the 'Safe Drive, Save Life' campaign of the state government.
West Bengal Chief Minister Mamata Banerjee ordered an inspection of the bridge from which the bus fell into the canal.
The chief minister, who had visited the spot soon after the incident and stayed in the town overnight, told reporters, "An inspection of the condition of the bridge must be conducted. And speed breakers must be installed in and around the area... That is really needed".
"We had completed handing over the bodies to family members by midnight," she said, referring to the 36 bodies pulled out yesterday.
"The DM has already distributed Rs five lakh to each family as we had announced," Banerjee added.