The Department of Energy and Climate Change (DECC) said: "Current estimates are that the spill could be of several hundred tonnes".
A spill on that scale would be the worst in the North Sea since 2000 when more than 500 tonnes was spilt, according to DECC data.
Shell said around 216 tonnes of oil, equivalent to 1,300 barrels, had leaked into the North Sea in a "significant spill".
"Work continues to stop the oil remaining in the flowline from leaking. We estimate the current rate of leakage is less than five barrels a day," the oil major said in a separate statement on Monday.
Oil from Shell's Gannet field has been spilling into the sea since last Wednesday, but the rate has been falling since the company shut off the well the same day.
By comparison, almost 5 million barrels gushed into the Gulf of Mexico from BP's blighted Macondo well last year.
"In the context of the UK Continental Shelf, the spill is substantial," a spokesman for the DECC said, noting assessment of the size of a spill is subject to revision. "They (Shell) are working to completely halt any further leakage."
Shell said the incident was a "significant spill in the context of annual amounts of oil spilled in the North Sea".
"We have taken it very seriously and responded promptly to it," the company said.
The DECC echoed Shell's expectation that the oil sheen will not reach the shore, because it is being dispersed naturally by waves. Shell has equipment on standby to use if required.
Shell's shares were trading up 0.35 percent to 2,015 pence at 1528 GMT, lagging the European index of oil and gas companies, which was 0.8 percent higher.
"We don't know how much has spilled, but it seems to be contained at this point. It has a negative impact but it's a relatively small impact," Macquarie analyst Jason Gammel said.
Traders downplayed the impact of a shutdown at Gannet, which Shell co-owns with US major Exxon , on oil supplies, saying it was a small field and would not cause much disruption.
The oil sheen from the leak, 180 km off the Scottish port of Aberdeen, covered around 37 square km, said Shell's spokesman.
Environmentalists Greenpeace and the Royal Society for the Protection of Birds (RSPB) complained about a lack of information.
"Thousands of young razorbills, puffins and guillemots are flightless and dispersing widely in the North Sea during late summer, so they could be at serious risk if contaminated by this spill," Stuart Housden, director of RSPB Scotland, said in a statement emailed to Reuters.
A spokesman for the Scottish government said fishing boats continued to operate.
"It hasn't had much of an impact, other than that Marine Scotland has notified fishing vessels to stay clear of the affected area," he told Reuters.
Government data showed there was a reduction in significant hydrocarbon releases in UK waters in 2010-2011 from the previous year, though a parliamentary report in January questioned the country's readiness to tackle a major oil spill.
Shell said it plans to issue a further statement about the leak later on Monday.
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Don't worry Shell can buy ads in all major publications to show how green it is. It has successfully done that while plundering Nigeria. I remembered correctly how there were load of ads in Times, Newsweek and Economist after the Nigeria story got leaked about its opponent executions and oil spills.