The prime minister has been "crystal clear" about how the refurbishment of his Downing Street flat was financed, the foreign secretary has told Sky News.
But another senior Conservative, the party’s leader in Scotland, has said the PM should quit if he is found to have breached the ministerial code.
Asked if Mr Johnson should resign if such a development comes to pass, Douglas Ross told the BBC’s Andrew Marr Show: "Of course, I think people expect the highest standards of those in the highest office of the land."
Standards adviser Lord Geidt is looking into the matter and is expected to rule on whether the PM broke code.
But the code states that the PM is "ultimate judge of the standards of behaviour expected of a minister and the appropriate consequences of a breach of those standards".
Mr Raab said the electorate and voters have "ultimate accountability" over Mr Johnson.
Earlier this week, the PM claimed there was not "anything to see here" as questions swirl over who paid for his Downing Street flat renovations.
Mr Johnson has repeatedly said he paid for the refurbishment of the private flat above Number 11.
But he has refused to answer whether he paid for the initial cost or whether a donor or the Conservative Party funded it and he paid the amount back.
Both Number 10 and the Conservative Party have not denied reports that the Conservative Campaign Headquarters (CCHQ) paid the Cabinet Office to cover initial costs of the works.
The furore has sparked a number of inquiries, including from the Electoral Commission into whether any donations or loans were properly declared.
It has said there are "reasonable grounds" to suspect an offence or offences had been committed.
But the foreign secretary defended the PM’s handling of the issue, telling Ridge: "I think the prime minister has been very clear and we’ve got, for any questions not yet answered, there are three reviews, the prime minister has set up some of them, is engaging fully with all of them.
"I think the right thing to do is to respect the integrity of them, let them run their course and they will resolve any outstanding questions people have."
Pushed to say who initially paid for the work, Mr Raab did not answer and instead reiterated his defence of Mr Johnson.
"The prime minister has been very clear, he covered the costs himself, he has followed all the codes of conduct, he has taken official advice," he said.
"Frankly, I don’t know any of the other details of it and there are a few reviews that will look into those questions and the prime minister and the government of course embrace the transparency and the integrity of those processes."
But he declined to deny a report in the Sunday Times that a second invoice for lavish renovations of the Prime Minister’s Downing Street flat may have been settled by a Tory donor.
And Mr Raab said he had "no idea" if a party donor was asked to pay for the PM’s childcare costs.
The donor is alleged to have said: "I don’t mind paying for leaflets but I resent being asked to pay to literally wipe the prime minister’s baby’s bottom."
"You don’t have conversations like that with the PM," the foreign secretary said when asked about the report.
"I can’t comment on every little bit of gossip that’s in the newspapers.
"The last thing you asked me about, I think, is an example of tittle tattle."
A Number 10 spokeswoman said Mr Johnson had "covered the cost of all childcare", but did not respond when asked if he paid for the original bill or had reimbursed somebody else.
Labour frontbencher Lisa Nandy said it was clear that the PM was "withholding information" from the public.
"It’s appalling we are in a position where he won’t come clean about who loaned him money or gave him money, and what favours or promises may have been given in return," the shadow foreign secretary told Ridge.
Ms Nandy claimed Mr Johnson "thinks that the rules don’t apply to him and his friends", adding: "We need to know who the prime minister is beholden to, we need to know what he has promised in return.
"If the prime minister is beholden to other people, who is he not serving? That’s the people of this country.
"This is about integrity, it’s about trust, and it’s about whether there’s one rule for them and one rule for everyone else."
The row comes ahead of local elections next Thursday in England, as well as elections for the Scottish and Welsh parliaments.
In a sign that the refurbishment row may be having an effect on public opinion, two new polls suggest the Tory lead over Labour has shrunk.