Finance Minister Jane Hutt said the 2016/17 draft budget would back Labour’s “principles and priorities”.
She claimed the Welsh government faced a 3.6% cut in UK government fundingover five years, once the effects of inflation were taken into account.
Ms Hutt said the aim was to support key public services while also encouraging business.
The lion’s share of the Welsh government’s £15.3bn budget comes from the UK Treasury, apart from about £1bn raised in business rates.
Ms Hutt added: “The message of this ‘fairer, better Wales’ budget today is about ensuring that we do support these public services that mean most to the people of Wales, but also that we enable business to progress for a buoyant and prosperous economy.
“It’s tough in terms of how then you divvy out the money in terms of our spend.”
Almost half of the Welsh government’s budget is spent on health, which is set to increase from 46% to about 48%.
Health spending in Wales has seen above-inflation increases since October 2013, when the Welsh government reversed its controversial decision not to protect the NHS budget between 2011 and 2013.
Current NHS spending is still lower than it was in 2011, once inflation is taken into account.
BBC Wales also understands that cuts to council budgets will not be as severe as expected.
The body representing local councils said they would “welcome” any settlement better than the 4% cuts they faced in 2015/16.
Chris Llewelyn, deputy chief executive of the Welsh Local Government Association, said: “Any increase in funding, any improvement, will result in investment in services like social services and education, so any improvement is good news for local government.”
Liberal Democrat support to pass the £15.3bn budget is expected as part of a two-year deal agreed with Labour in 2014.
As Labour does not have an overall majority in the Senedd, it needs support from at least one opposition party to get the budget passed.