Ms Sturgeon told the BBC such powers would allow the Scottish government to grow the economy.
She added that she had spoken “briefly” to Prime Minister David Cameron but more discussions were required.
Ms Sturgeon also said her party now provided the main opposition at Westminster.
Labour, with 232 MPs, are the official opposition but Ms Sturgeon claimed her party, which gained 50 MPs on Thursday, was the one putting pressure on Mr Cameron’s Conservative government.
The SNP is the third largest party in the UK despite only standing in Scotland.
It took 56 of the 59 seats in Scotland, reducing Labour to just one MP when they had previously had 41.
Speaking to the BBC’s Andrew Marr programme, Ms Sturgeon said Mr Cameron did not appear to want to move beyond powers already outlined in the Smith Commission, which was formed after the independence referendum to fulfil the pledge to give Scotland further devolution.
She said: “What we will argue for is priority devolution of powers over business taxes, employment, the minimum wage, welfare, because these are the levers we need to grow our economy to get people into work paying taxes and lifting people out of poverty.
“David Cameron did not give me any indication that he wanted to move beyond the current Smith Commission proposals.