The announcement follows a string of gaffes and resignations that rocked the Green Party last week.
"This is a serious situation. Sweden needs a strong green party," Fridolin told reporters at the Monday morning press conference. "We’re prepared to hand over responsibility if the nominating committee feels others are better suited for the job.”
The Greens will meet for their party's convention in three weeks' time. Romson and Fridolin said they will let the party determine if they should remain at the helm.
"In a crisis of this kind, the party needs to have a debate in order to get a fresh start," Romson said. "That will come at the party conference."
Fridolin and Romson said the party's "politics need to be sharpened and the leadership needs to be tried". However, the two want to remain at the helm and Romson said: "We believe that both of us can come out of this stronger."
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.
The Green Party conference, which Fridolin and Romson say will mark the party's "fresh start", is scheduled to take place May 13th to May 15th in Karlstad, west-central Sweden.