Mr Brown said he was "very angry about what has happened" on MPs' expenses.
In a speech as he launched Labour's European election campaign, he said: "Where there is irregularity now it has got to be dealt with immediately. Where standards have been transgressed and the evidence has been shown to be there, action has got to be taken.
"Where disciplinary action is necessary, it will and will immediately be taken."
I deeply apologise for such sloppy accounting in a very loose and shambolic allowance system but there is nobody to blame but myself and I take full responsibility for this
He added: "If there are any other disciplinary cases where we have to take action we will take action immediately."
Mr Morley has not had the whip withdrawn, which would effectively expel him from the Parliamentary party - but Labour chief whip Nick Brown made it clear that he faced expulsion if he failed to clear his name.
He has also been suspended as the prime minister's climate envoy but remains chairman of the energy and climate select committee.
Nick Brown said his case would be discussed by the party's ruling National Executive Committee next Tuesday but told BBC News he wanted to give Mr Morley "breathing space" while the allegations were investigated.
The chief whip said Mr Morley had first come to him "a week or two weeks ago" to say there might be a problem with his expenses, but he denied he should have acted sooner, as he did not know the full details at that stage.
Mr Morley, who is MP for Scunthorpe, has referred himself to Parliamentary Standards Commissioner John Lyon in an effort to clear his name.
According to the Telegraph, he claimed £800 a month for a Scunthorpe property for 18 months after the mortgage ended.
In a statement, Mr Morley said he did his accounts in "yearly bundles" and he had "simply let the established payment run as it has for some years".
We've been slugging this matter out for days and not got anywhere - we've failed as a political class
He added: "I deeply apologise for such sloppy accounting in a very loose and shambolic allowance system but there is nobody to blame but myself and I take full responsibility for this," he added.
The Telegraph also alleges Mr Morley rented out a London flat designated as his main residence to another Labour MP, Ian Cawsey, a close friend and former special adviser.
Mr Cawsey named the property as his second home, allowing him to claim £1,000 a month to cover the rent which he was charged by Mr Morley.
In November 2007, the newspaper claims, Mr Morley "flipped" his designated second home from his Scunthorpe property to his London home and for four months the two men claimed expenses on the same property.
Tory aide quits
The Commons fees office stopped the arrangement. Mr Cawsey said he had been unaware of Mr Morley's financial arrangements.
Mr Morley issued a lengthy explanation of his arrangement with Mr Cawsey in which he denied any wrongdoing and said he used the money from his Labour colleague to reduce his claim to the taxpayer.
Chief Whip Nick Brown has also spoken to Labour MP Fabian Hamilton, who claimed thousands of pounds in second home allowances for his family home in Leeds while listing his mother's property in London as his main residence.
People in Elliot Morley's constituency react to his expenses revelations
The Leeds North East MP said those claims covered a two-year period while he was looking after his mother in London. He told the BBC his mother was dying and he had to spend "a huge amount of time" at the house where his family had joined him.
"The Inland Revenue were quite satisfied that I'd spent more time in that house over those two years and I was paying the costs of maintaining that property as well, a big four bedroom property," he said.
"So it was not unreasonable to ask for help with my other home which was in Leeds."
Nick Brown said the expenses scandal had done "extensive damage to the reputation of Parliament" - but he accused the Conservatives of blocking a cross-party agreement on reforming expenses and of "trying to play politics for all it is worth" over the issue.
He said there would not be wholesale reform until Sir Christopher Kelly, chairman of the committee on standards in public life, completed his report later in the year.
Tory leader David Cameron is setting up his own scrutiny panel to investigate Tory expense claims.
The first casualty of the clampdown was his own Parliamentary aide, Andrew MacKay, who quit his post over what the party said were "unacceptable" expenses claims.
He claimed the second home allowance on his London address, while his wife, Tory MP Julie Kirkbride, claimed it for another home.
Between them they claimed 98.5% of the total allowance available to them since 2004.
He has said he will pay back an amount decided by the Tory panel, adding: "Due to an error of judgement in accepting advice from the fees office I have let a lot of people down."
Mr Cameron has said he will seriously consider Sir Christopher Kelly's recommendations when they are published in the autumn but has urged Gordon Brown to show leadership and push through reforms of the system now.
Liberal Democrat leader Nick Clegg has written to Mr Cameron and Mr Brown to say it is time all the parties agree to accept the Kelly inquiry recommendations in full when they come out.
He said: "We've been slugging this matter out for days and not got anywhere," adding: "We've failed as a political class."
He said the latest developments in the expenses saga were "a further deterioration of trust in public politics".
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