Griffith, appointed shadow chancellor last month, told the BBC that Labour had raised taxes at its last two Budgets and warned that “the pips are well and truly squeaking”.
Saying he would rule out tax rises, he argued that the government should “pause job-destroying red tape”, adding: “Whatever its intentions, it is causing a real chill in the vacancy market.”
The Conservatives cited figures from the Federation of Small Businesses estimating that tax compliance costs small businesses £25bn a year and that the average small business spends 44 hours each year on tax administration.
The party has appointed Lord Mackinlay of Richborough, the former South Thanet MP, and Robert Colvile, the outgoing director of the Centre for Policy Studies think tank, to produce a report on reducing regulations for small businesses.
Griffith said governments must “balance the books” and that Conservatives would reform the welfare system, reduce spending on foreign aid and cut “some of the central cost of Whitehall” to save money.
The Mail on Sunday reported over the weekend that Conservatives could promise to abolish inheritance tax if they win the next election, with the policy potentially being announced at the party’s annual conference in October.
Asked whether he would pursue such a move, Griffith said there was “work to be done” and added: “We’ve got to fully find the money.”
He said he wanted to be responsible and make only promises he could keep.
Griffith also said he had recently visited Sweden, which abolished inheritance tax in 2005.
Reform UK has previously said it wanted to reduce inheritance tax, but Treasury spokesman Robert Jenrick told a Reform conference fringe event that it would not be a priority.
“It’s a bold chancellor who would say they would rather privilege 36,000 families than 40 million income taxpayers,” he said.
Asked whether abolishing inheritance tax would amount to a tax cut for the wealthy, Griffith argued that it would boost growth and that the richest people were often able to “arrange their affairs” to avoid the tax.