An investigation has been launched after an alert at the Torness nuclear power station on Thursday night.
Torness said the public had not been at risk
Willie Waddle, director of the East Lothian plant, said debris prevented a spent fuel element being properly located in position.
He said no-one was injured or at risk from radiation during the incident and that the plant was continuing to generate power as normal.
Nationalists, the Greens and Friends of the Earth have all voiced concerns.
Lothian and Borders Fire and Rescue were alerted at about 2050 GMT on Thursday.
The service said that it sent its standard response of six normal pump fire engines and four specialist units to the site.
British Energy, which operates the plant, said that the emergency services were called in as a precaution, but there was no major panic.
Mr Waddle said that the incident had been confined to the fuel pond.
He told BBC Radio's Good Morning Scotland programme: "We stood down the emergency at half-past-four this morning, we have been taking measurements and there have been no radiation leaks at all."
He said debris which had made its way into the fuel handling area had prevented the element from fitting properly into its container.
"It shouldn't be there, we are surmising the debris will be graphite sleeves from elements, it will be slightly radioactive as it surrounds the fuel element, but there is no risk to anybody on or off the power station."
Mr Waddle said the investigation to find out how the debris appeared in the container could take a number of days.
British Energy said the alert had no effect on electricity generation at Torness and that the 38 staff on the late shift were checked, accounted for and continued with their normal work.
Environmentalists and politicians opposed to nuclear power expressed concerns.
Duncan McLaren, of Friends of the Earth Scotland, said: "This latest incident highlights just another reason why nuclear should be given no second chances in Tony Blair's forthcoming energy review.
"Nuclear power is unsafe, uneconomic and unnecessary. There are safer, cleaner and cheaper ways to tackle climate change."
SNP energy spokesman Richard Lochhead said: "It is extremely worrying when incidents like this occur.
"I would hope that the investigation will be thorough and the results made available to the public as they are put at risk when accidents like this occur.
"There is no need to gamble with the safety of thousands by creating new nuclear power stations when Scotland has a wealth of renewable and clean fossil fuel resources available."
Chris Ballance, Green MSP for the South of Scotland, also called for an open investigation into the incident.
He said: "I am very much relieved that the incident is not a threat to people or the environment.
"But I will be pressing for the results of an investigation to be made fully open to the public, and not having to be extracted through freedom of information requests as we had to do recently over another incident at the plant."
Mr Ballance said the alert was a reminder of the risks associated with nuclear technology.
"The last time they talked about a very minor incident at Torness it turned out to be a very large bang which shut the plant down for six to nine months," he said.
However, local Labour MSP John Home Robertson attacked the Green MSP for "opportunistic criticism".
"Far from this incident being a sign of the dangers of nuclear power, the precautions taken last night ably demonstrate the very high safety standards which the UK nuclear industry conforms to," said Mr Home Robertson.
"I'm delighted that the power station has been able to continue generating carbon-free electricity despite this incident and I commend the management and staff at Torness for the responsible way in which they've acted."
The power station is located on the East Lothian coast, five miles south east of Dunbar, close to the main A1 road between Edinburgh and Newcastle.
The emergency has fuelled opposition among nuclear critics
It emerged earlier this month that its lifespan was to be extended by decades.
It had been expected to close in 2023, but British Energy said that updating vital equipment could extend its operating life.
Torness opened in 1988 and employs nearly 500 people.
Safety incidents recorded at the site, and at Hunterston in North Ayrshire, have allegedly included unauthorised waste discharges and problems with reactor fuel and fires.
The environment and equipment at the sites have also been contaminated with radioactivity, according to a newspaper report earlier this month.
British Energy in 2003 was fined £15,000 for dumping radioactive waste from Torness into the North Sea.
Reactor 1 was closed down in August 2002 because of vibrations in the gas circulation system, which cooled the reactors