Matt Hancock said the technique was "cost-effective" and the Cabinet Office would look at how to pick up the bill.
The Lords had said switching from a parchment called vellum to archival paper could save about Â£80,000 a year.
It said it had not received an offer from the government department and so would proceed with the original plans.
"If the Cabinet Office write offering to take on the responsibility for printing Acts of Parliament on vellum, it would of course be considered.
"As of yet, that offer has not been made," a spokesman said.
Two copies are made of Acts of Parliament. One is stored in the National Archives and the other in the Parliamentary Archives.
Significant state documents - such as Magna Carta and thousands of Acts of Parliament - have traditionally been recorded on goat or calf skin.
MPs had handed the decision to end the practice to the House of Lords, which is responsible for the cost of vellums for Parliament, and peers decided to push ahead with the cost-cutting measure.
The House of Lords said vellum was "extremely expensive" and the cost of printing copies of laws on it - which it put at Â£100,000 a year "cannot be justified".
"Archival quality paper is an extremely high quality and durable alternative," said chairman of committees Lord Laming.
The Commons Administration Committee backed the Lords' proposal, saying it was "convinced by the arguments".
However, it encountered criticism from MPs, with Conservative James Gray calling for the "retrograde decision" to be reversed.
Mr Hancock told the Daily Telegraph: "Recording laws on vellum is a millennium-long traditions and surprisingly cost-effective.
"While the world constantly changes, we should safeguard some of our great traditions."
In 1999, the House of Lords decided in favour of scrapping the use of vellum - but the move was rejected in the Commons by 121 votes to 53, a majority of 68.
A centuries-old tradition of recording copies of Parliament's laws on calf skin will continue, a minister has said, after peers signalled its end.