Sir Keir Starmer and his wife Victoria accepted donations of clothing so they could “look their best” to represent the UK, David Lammy said.
The Foreign Secretary said other countries allowed lavish, taxpayer-funded budgets for clothing for their leaders.
The Prime Minister is alleged to have broken parliamentary rules by failing to declare donations of clothing for his wife within the designated time limit.
The gifts, from prominent Labour donor Lord Alli, were not initially declared in the register of MPs’ interests.
The Sunday Times reported that the Prime Minister approached the parliamentary authorities on Tuesday to make a late declaration after being given updated advice on what needed to be registered.
The Tories demanded a full investigation into the Starmers’ links with Lord Alli.
Mr Lammy told the BBC’s Sunday with Laura Kuenssberg programme: “The Prime Minister did declare funds that he received from Lord Alli, he’s then gone back to the Parliamentary Commissioner to further check details on some of those funds that have made their way to his wife.
“So he has done that, and he is seeking to comply with the rules. So this is not an issue of transparency. He is attempting to be transparent.”
He added: “I’ve just come back from the United States, where US presidents and first ladies have a huge budget paid for by the taxpayer so that they look their best on behalf of the US people. We don’t have that system over here.
“The truth is that successive prime ministers, unless you’re a billionaire like the last one, do rely on donations, political donations, so they can look their best, both in the hope of representing the country, if you’re in the Opposition, or indeed as prime minister.”
The US president receives a salary of around £305,000 (400,000 US dollars) and a £38,100 (50,000 dollar) expenses allowance, although there is no specific clothing budget.
Sir Keir had a high-profile legal career before entering politics and Mr Lammy said “I’m not suggesting the Prime Minister is broke”, but “successive prime ministers want to look their best – and their partners – for the country, that is what lies behind this”.
The Sunday Times reported the donations covered the cost of a personal shopper, clothes and alterations for Lady Starmer both before and after Labour’s election win in July.
MPs are required to register gifts and donations within 28 days.
A No 10 spokeswoman said: “We sought advice from the authorities on coming to office.
“We believed we had been compliant, however, following further interrogation this month, we have declared further items.”
The guide to the Commons rules states MPs should register “any benefit given to any third party, whether or not this accompanied a benefit for him or her, if the Member is aware, or could reasonably be expected to be aware, of the benefit and that it was given because of his or her membership of the House or parliamentary or political activities”.
Lord Alli’s involvement with the Labour leader has already proved controversial after it emerged he had been given a Downing Street security pass without apparently having a Government role.
The row was dubbed the “passes for glasses” affair because Lord Alli has previously donated tens of thousands of pounds worth of clothing, accommodation and “multiple pairs” of spectacles to the Labour leader.
A Conservative Party spokesman said: “It’s taken just 10 weeks for Keir Starmer to face an investigation for his conduct.
“After facing allegations of cronyism and now apparent serious breaches of parliamentary rules there must be a full investigation into the passes for glasses scandal.
“No doubt the millions of vulnerable pensioners across the country who face choosing between heating and eating would jump at the chance for free clothes just to keep warm in the face of Labour’s cruel cut.”
Tory leadership hopeful James Cleverly told Sky News: “What we have got to recognise is Keir Starmer and Sue Gray (his chief of staff) have been very, very critical of Conservatives over exactly this – now if your position is that, well, ‘these things happen’ and we should be thoughtful and flexible in our response, that’s fine.
“But if, like Keir Starmer, you have been really aggressive in your criticism of Conservatives for this, then you’ve got to make sure that you are totally above reproach, and he’s failed to do that.
“So I think it’s absolutely legitimate that we point out the hypocrisy of someone who basically got his job by criticising others for what he’s now doing.”
