Treasury minister John Glen made the assurance after he faced appeals from MPs to ensure thousands of the firm’s customers “don’t miss out on a dignified” funeral.
The company went into administration earlier this year, with its website saying “it is uncertain that the funeral plans (of customers) will be able to be fulfilled”.
Mr Glen said: “The important thing is that we give reassurance going forward, but there will be a day of reckoning for the directors of Safe Hands to account for what happened, but the administration process is what must happen first.”
He was responding to the issue being raised in the House of Commons by independent MP Margaret Ferrier, who described the company as “unscrupulous” and its actions as a “scam”.
She urged the Government “to find a way to make sure that these people who have lost hard-earned money don’t miss out on a dignified goodbye when that time sadly comes”.
The company had more than 45,000 customers when it went into administration.
The Financial Conduct Authority is due to oversee the unregulated funeral plan market in July as part of a major overhaul of the sector.
Ms Ferrier said: “I wholeheartedly welcome the Government’s plans to bring funeral planning services under the remit of the Financial Conduct Authority in July this year.
“The plans… will hopefully protect future customers from falling victim to the scams of unscrupulous companies like Safe Hands.”
Describing the situation, she said the customers’ money was put into a trust and then reinvested, saying it was sold as protecting customer investments.
Ms Ferrier went on: “Administrators found a significant shortfall between the value of this trust and the cost of the funeral plans it would need to finance. Seemingly what administrators found is that the trust’s assets had been wildly overvalued.
“Even more concerningly that most of the assets were actually owned by third parties.”
She added: “Reports indicate that over £60m of the trust’s reported £64m valued assets were high-risk investments based offshore. And if true, we are talking about fraudulent misappropriation of the trust’s assets.
“I will refrain from speculating who might have benefitted from all of this, which can only be described as a scam.”
SNP MP Peter Grant (Glenrothes) said the firm’s failure left behind “chaos”.
Mr Glen said it is “right that the Government acts to protect consumers” with a “robust, proportionate regulatory framework”.
He went on: “In addition to a well-regulated market, we will promote effective competition and drive better long-term outcomes for consumers.
“As I have said, Safe Hands customers can be assured that they will be covered for at least another six months. And I encourage other providers and market participants to take further action as Dignity have done to protect consumers of firms that won’t become authorised.
“But I would like to assure the House that the Government and the Financial Conduct Authority continue to work closely with each other and with the sector.”
He said Dignity, one of the country's largest funeral plan providers, has stepped in to provide funerals on behalf of Safe Hands customers in the immediate period after the company went into administration and agreed to do so for a further six months.
He concluded: “We all have a moral obligation to ensure that funeral plan customers and their loved ones receive the certainty that they need and deserve.”
“It is very distressing for its customers and their families.”