Derek Mackay has issued the calls as Chancellor Philip Hammond warned that he is ready to introduce an "emergency Budget" in the event of a No Deal Brexit when the UK leaves the EU next March.
The Scottish Government wants a "meaningful uplift" in public services funding and is also concerned about the roll-out of Universal Credit.
"This statement must be backed up by concrete actions to provide a meaningful uplift in funding for public services, in addition to the funding increases announced for the NHS being delivered as a true net benefit and not offset by other cuts to the Scottish budget.
Read more: Why Brexit means austerity will continue"In a letter to the Chancellor this month, I asked for the roll-out of Universal Credit to be postponed until the flaws are fixed, a position supported by the Public Accounts Committee this week. Yet as we're promised an end to austerity, the UK Government continues to press ahead with this damaging policy.
"This year, working Universal Credit claimants in Scotland will lose £164 million, and around £245 million by 2021. We have repeatedly called for a halt to the roll-out until it can be proved not to cause further hardship."
Mr Hammond has warned that the Government will have to adopt a new economic strategy if Britain leaves the European Union without a deal with Brussels.
On the eve of the Budget, Mr Hammond said he would have to tear up his plans for the economy and set out a new Budget if there was no Brexit deal when the UK leaves the bloc in March 2019.
"If we were to leave the European Union without any deal - and I think that's an extremely unlikely situation but of course we have to prepare and plan for all eventualities as any prudent government would - if we were to find ourselves in that situation then we would need to take a different approach to the future of Britain's economy," he told Sky News's Sophy Ridge on Sunday programme.
"We would need to look at a different strategy and frankly we'd need to have a new Budget that set out a different strategy for the future."