A portion of the tank had collapsed, they added.
The firefighters had initially succeeded in bringing the blaze under control, but "excessive heat" had led it to reignite at around 4.30 am yesterday.
A senior Bharat Petroleum Corporation Ltd (BPCL) official said the blaze in tank number 13 was still continuing.
"The intensity of the heat has come down slightly compared to what it was in the morning. The tank has collapsed a bit inwards but the fire is contained within it and is in control," BPCL executive director Manohar Rao told PTI.
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Vessels bring crude and other commodities and offload the same at the Jawahar Dweep anchorage, which is stored in tanks and then ferried to the nearby refineries through underwater pipelines.
Officials had yesterday exuded confidence that the blaze would be completely doused by this morning.
"It is a matter of time now that the residual product inside the affected tank is burnt completely and the fire gets extinguished," Rao said.
He informed that teams from the MbPT, Mumbai Fire Brigade, CIDCO and oil marketing companies led by BPCL were engaged in the fire-fighting efforts.
No casualty was reported during the mishap, which is suspected to have been caused due to lightning.
Rao clarified that there would not be any shortage of HSD (high-speed diesel) in the market due to the fire incident.
The fire had broken out when Mumbai and surrounding areas witnessed thundershowers.
MbPT Chairman Sanjay Bhatia had said the blaze was contained to one tank farm owned by the BPCL.