Jacqui Smith says she has fully complied with parliamentary rules
Jacqui Smith has said her decision to claim "second home" expenses for her family home was "above board" and approved by the Commons authorities.
Ms Smith reportedly claimed £116,000 in expenses for her Redditch home after telling the Commons that her sister's London home was her main residence.
The home secretary said she had "received assurances" from the Commons authorities that her conduct was right.
The Conservatives said on Monday that she "may have questions to answer".
A formal complaint has been made to the parliamentary standards watchdog about Ms Smith's behaviour.
The Standards Commissioner said it had received the complaint - from pressure group Centre for Open Politics - but made clear it had not decided whether to look into the issue.
According to the Mail on Sunday, Ms Smith has claimed more than £116,000 in second home expenses, known as the Additional Costs Allowance, over several years.
It has been reported that Ms Smith stays at her sister's home when she is London, normally between Monday and Thursday.
The allowance is to help cover the cost of MPs having to have a second home - or place to stay - in London if their constituency is too far away to allow commuting to Parliament.
It can cover mortgage interest, fuel bills and things like a new kitchen, bathroom or even the purchase of items such as flat screen televisions and fridges.
The rules state that the main residence is where the MP "spends more nights than any other".
Under the rules, which have been in the spotlight over the past year, Parliament leaves it up to MPs to decide whether their London or constituency home is their "second home".
In a statement on Tuesday - her first since the controversy arose - Ms Smith said she had checked with the Parliamentary authorities that her expenses arrangements were in order and had been assured they were.
"I have abided by the rules," she said. "Everything I have done is above board."
Speaking during a visit to domestic violence charity Refuge in central London, she said: "The thing with being MPs is we have to live in more than one place.
"I have always been very clear with the authorities about the arrangements that I made. I specifically asked whether or not the home where my children live had to be my main home. I received assurances it didn't have to be.
"Because we live in two places, that's why we make the arrangements that we do."
A No 10 spokesman came out in support for Ms Smith on Monday, saying she had explained her actions and that they had been verified by the Commons authorities.
But Mr Cameron said it was right that Ms Smith should be expected to justify her arrangements as "reasonable".
"There are rules and you have to meet both the letter and the spirit [of the rules] and explain in a reasonable way 'this is the arrangement I have and I think it is a reasonable one'."
The Lib Dems have said they will ask the Commons authorities to look again at the designation of first and second homes.
The rules over designating a main residence were recently clarified after a complaint about Ms Smith's cabinet colleagues Ed Balls and Yvette Cooper.
They were cleared in October of any wrong-doing over earmarking their constituency home in Yorkshire as their main residence rather than their London home.
In his ruling on that case standards commissioner John Lyon said it was difficult to determine which home MPs should claim as their main home.
Mr Lyon concluded his report by saying that the "normal criteria" that the main home should be where an MP spends more nights than anywhere else should remain the "reasonable general test".