The two-year rule was introduced in an effort to clamp down on sham marriages and to put an end to so-called "wife imports".
But it has been blamed for forcing women to remain in abusive relationships, with a 2012 government-ordered inquiry recommending the rule be abolished.
According to Eva Eriksson, who carried out that inquiry on behalf of the former equality minister, Nyamko Sabuni, thousands of newly arrived women seek help every year after being assaulted by their Swedish spouses.
Eriksson, who is the governor of Värmland in west Sweden, claimed that the two-year rule locks women and their children into abusive relationships.
But Arnholm, who replaced Sabuni as equality minister in January 2013, has defended the rule.
"I think it serves its purpose," Arnholm told newspaper Svenska Dagbladet.
"It makes it simple and possible for people who fall in love to quickly be able to be together and to live in the same country. I know that many people appreciate [the rule]. Removing it would have sad consequences."
Arnholm did concede that there are some problems with the two-year rule.
"It should not be a protective shell or a pretext for battered women to stay with their men. We have to, at all costs, avoid the feeling that one gets thrown out of Sweden if one leaves an abusive man. But that does not lead me to conclude that the two-year rule should be abolished."
As part of the 2012 inquiry, Eriksson spoke to social services, police, hospitals and women's refuges.
She concluded that the extent of abuse suffered by women who came to Sweden to marry a Swedish man was widespread.
The report was welcomed by The National Organization for Women's Shelters and Young Women's Shelters in Sweden (Roks).
The Centre Party's Women's Association has also demanded that the two-year rule be scrapped, with its president, Gunilla Hjelm, urging Arnholm to take "immediate action" against "the practice of wife importation".
She said it "puts thousands of women in vulnerable positions".
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