The right-wing government had in its 2017 budget bill in September predicted that it would withdraw 225.6 billion kroner (24.2 billion euros, $26.2 billion, at current exchange rates). But that number has now been shaved down to 220.9 billion.
"Unemployment is on its way down and growth is picking up," Finance Minister Siv Jensen said in a statement.
The Scandinavian country, the biggest oil producer in western Europe, has suffered from the drop in oil prices since mid-2014.
The economic upswing -- sustained by low interest rates, a weaker krone and an expansionary budget policy -- is good news for Norway's Conservative-led coalition government as it gears up for difficult legislative elections in September.
Mainland gross domestic product -- excluding the shipping and oil-and-gas sectors -- is expected to grow by 1.6 percent this year and 2.4 percent next year, after posting meagre growth of 0.8 percent in 2016, the revised budget bill showed.
In another sign of recovery, unemployment is expected to shrink to to 4.3 percent in 2017 and 4.1 percent in 2018, down from the 4.7 percent registered last year.
The government's proposal would amount to tapping 2.9 percent of the fund's total value as estimated at the beginning of the year.
That is lower than the 3.0 percent maximum proposed in February by the government, a cut from the current 4.0 percent rule.
On Thursday, the fund, the world's largest sovereign wealth fund, was worth 8.06 trillion kroner. It is invested in stocks, bond and real estate around the world.
The minority government must now negotiate with its centre-right allies to get its budget bill adopted by parliament.