Several male senators - Bob Casey (D-Pa.), Joe Donnelly (D-Ind.), and Sherrod Brown (D-Ohio) - have also called for the senatorial colleague to resign as well.
The Minnesota Democrat's office said he would make an announcement Thursday, but did not specify the subject.
Democratic Massachusetts Congressman Seth Moulton said on "Meet the Press Daily on MSNBC on Tuesday that he thought Frankin should step down".
Democratic Gov. Mark Dayton, who served on the U.S. Senate Ethics Committee during his single term in Congress, said that panel is the proper place to decide Franken's fate. "This morning I spoke with Sen".
"Today, I am calling on my colleague Al Franken to step aside", Hirono wrote on Twitter. The wave of allegations began with Leeann Tweeden, who said that Franken aggressively kissed her while they were overseas entertaining the troops and groped her in her sleep.
"He was between me and the door and he was coming at me to kiss me", she told Politico.
King issued a statement Wednesday afternoon calling on Franken to resign as well. "Everyone must share the responsibility of building a culture of trust and respect for women in every industry and workplace, and that includes our party".
"For me, I think it's time for my friend to resign", King said in a statement.
Kirsten Gillibrand was the first to call on her fellow Democrat to step down. Multiple women have accused Moore of sexual misconduct with them when they were teens, including one who said Moore molested her when she was 14.
The woman, who spoke to Politico, claims the Minnesota Democrat pursued her after her boss had left and she was collecting her things. Franken, she said, pulled her close when her husband offered to snap a cell phone photo of them, and "as my husband took the picture, he put his hand full-fledged on my rear", Menz said. A fourth woman, an Army veteran, alleged Mr. Franken cupped her breast during a photo op on a USO tour in 2003.
Franken describe behavior that can not be tolerated.