Romson and Fridolin, de facto leaders of the Greens and ministers within Löfven's government, told reporters they would leave it up to the party's nominating committee during the next party convention to decide whether or not they should stay on.
Their announcement follows a string of gaffes and resignations that rocked the Green Party last week.
Speaking on Monday, Löfven would not say whether Romson, Sweden's vice PM and environment minister, and Fridolin, the education minister, would continue in their roles if not re-elected by their own party.
"I'm not going to speculate on that," Löfven told a reporter. "I think it's natural that they are seeking this mandate from their party after this difficult week. And I also know that they have strong support."
The Green Party conference, which Fridolin and Romson say will mark the party's "fresh start", is scheduled to take place May 13 to 15 in Karlstad, west-central Sweden.
The prime minister also sought to shield his government from any political fallout suffered by the Greens, saying his governing partner's scandals and setbacks haven't hurt the efforts of his coalition government.
"It's clear the Green Party had a difficult week," Löfven said. "But the government's work continues. We're underway with our work on Swedish society. To lower unemployment, improve school results and strengthen the welfare system."
Reporters also asked if Löfven regretted forming a government with the Greens given what has happened in the past couple of weeks. He said all parties suffer through crises at one time or another and that he is confident the Greens would remain in government.
Last week, the Green Party hit a rough patch after party member and housing minister Mehmet Kaplan resigned, partly over comments he made in 2009 that compared Israel's treatment of Palestinians to that of the Jews' treatment in 1930s Germany. It also transpired that he had dined with leaders of extremist right-wing groups.
Two days later, local Green Party politician Yasri Khan quit after he refused to shake hands with a female television reporter, saying it violated his Muslim faith.
On Sunday, the party postponed a crisis meeting since there were concerns that outsiders had acquired the code needed to tune into the telephone conference.
The resignations and blunders cast a shadow over the party, which entered government for the first time in 2014 in a coalition with the Social Democrats. Fridolin and Romson have been criticized for how they handled the turbulence.