The change of stance by the party, the largest in the coalition government, means that the paragraph will probably be abolished in parliament Friday, reports DR.
The contentious, 151-year-old law criminalises acts such as burning the Qur'an or Bible.
But Venstre has now turned back on its previous position against abolishing the paragraph.
“We have agreed that we support the proposal to abolish the blasphemy paragraph from criminal law,” the party's political spokesperson Jakob Ellemann-Jensen said to DR Tuesday.
Paragraph number 140 in Denmark's criminal code states that “persons carrying out public insults or denigrating, in this country, lawful religious teachings or worships, may be punished with fines or imprisonment up to four months”.
Several of the party's MPs have previously stated their opposition to the removal of the anti-blasphemy clause and also opposed the change of stance now announced.
Arguments in favour of repealing the paragraph put forward by the party include recommendations by both the EU and Council of Europe to remove the paragraph, as has been done in a number of other countries without serious consequences.
“Some of what has pulled us in the other direction is whether it is necessary for us always to be able to say anything to each other, regardless of whether we tread on each other's feelings. Do we feel that is necessary at the moment? Do we think the tone of public debate is too nice? Do we need a degradation of that? These are many of the things we have discussed,” said Ellemann-Jensen.
Despite the diversity of opinions within the party, all Venstre MPs will vote to remove to remove the paragraph, reports DR.
The Danish blasphemy law debate has seen both security and free speech discussed.
Danish police security agency PET (Politiets efterretningstjeneste) concluded that the risk of terror attacks in Denmark could increase without the paragraph, DR reported in April.
In the same month, the populist Danish People's Party and left-wing Red Green Alliance (Enhedslisten) proposed the abolition of the blasphemy paragraph.
Conservative minister Søren Pape Poulsen said following the parliamentary proposal that “if we didn't have a blasphemy paragraph today, then we probably wouldn't make one either.”
Poulsen said at the time that he would take a closer look at the implications of removing the paragraph, noting the security concerns highlighted by PET.
The parliamentary discussion came after the paragraph was used to press charges against a man who published a video of the Qur'an being burned on Facebook, according to DR's report.
The most recent use of the paragraph to press charges prior to that incident was in 1971.
Poulsen's position was criticised by Danish People's Party justice spokesperson Peter Kofod Poulsen.
“This is relying on a security argument. It's weak. Every time something happens in the world, our leaders stand together and agree that it must not damage our values and our freedom of speech,” DR reported Kofod Poulsen as saying during the parliamentary debate.
But the Venstre U-turn now leaves the Social Democrats as the only parliamentary party now in support of retaining the paragraph.
Social Democrat spokesperson for religion Karen Klint told DR that the likely abolition of the paragraph left her feeling uneasy.
“I have always seen the blasphemy paragraph partly as a paragraph that is rarely used, but nevertheless provides a protection for the tone in debates on religion, which can be very tough and sometimes ugly and sensitive,” she said.
Klint said that she felt the relevance of the paragraph was not just related to freedom of speech.
“We also have that [potential prosecution for making offensive statements, ed.] in the racism paragraph. There are other things where freedom of speech comes under certain frameworks.
“Faith is one of the most sensitive things there is, and world history shows that people react differently when their faiths are insulted. That's why I'm uneasy about as now giving a free pass to say anything we want,” she added.