Rasmussen made the announcement on Tuesday at a hastily-arranged press conference in which he presented his government's plans for the coming year.
Those plans do not include tax reforms including reductions to top-bracket rates or a change to the margin for the top tax rate (known as topskat in Danish).
“We must concede that we cannot realise our ambition to give families more breathing space in household costs,” Rasmussen said according to news agency Ritzau.
The government will instead focus on pushing through tax cuts for low income groups, improving the financial benefits for those moving from social welfare payments to salaried jobs.
Increased incentives for pension schemes will also be introduced, the PM said, citing that support from parliamentary ally the Danish People's Party (DF) was already in place over this issue.
“Back in 2015, we agreed with DF on a limit on unemployment social welfare [kontanthjælpsloft] and welfare for refugees [integrationsydelse].
“We also agreed that the money released by this would be used to make it more attractive to take low-paid work,” Rasmussen said.
“The government has now reached the conclusion that, to achieve a good start to 2018, we would rather focus on that,” the PM continued, according to Ritzau's report of the press meeting.
The announcement by Rasmussen appears to be a blow for libertarian coalition partner Liberal Alliance, for which tax cuts are a core party issue; as well as the anti-immigration DF, which had hoped to secure major changes to Denmark's approach to refugees and asylum seekers in return for its support for tax cuts.
Liberal Alliance refused on Tuesday to see the development as a defeat.
“This is not a defeat. A defeat is when taxes go up,” party leader Anders Samuelsen, who is also foreign minister, said to Ritzau.
In December, Samuelsen's party threatened not to vote for the government's budget – which was eventually passed later that month – if Rasmussen did not deliver on tax cuts.
“We can conclude that there is currently no majority in parliament for easing taxes for normal, hardworking Danes,” the Liberal Alliance leader said to Ritzau on Tuesday.
“We still want to reduce income tax. We just can't do it right now,” he added.
“We still see the opportunity for something very politically important for the government to be traded for something very politically important for us, namely a paradigm change on immigration,” Dahl said to Politiken.
DF has proposed all refugees granted so-called temporary asylum (midlertidigt ophold in Danish) be denied the right to family reunification and returned to their home country as soon as it is considered to be safe, as well as for a refugee apprenticeship scheme known as IGU to be scrapped.
“Even though the government is downgrading its short-term ambitions with regard to tax policy, we are not downgrading our ambitions on immigration, so we will use other routes and the negotiations that arise during this government term to see how we are by other means able to achieve the things on foreigners and immigration that we think are completely necessary,” Dahl said to Politiken on Tuesday.