WASHINGTON — Some Democrats are “Ready for Hillary.” MoveOn.org is ready for Elizabeth Warren.

The liberal group is poised to spend $1 million on a campaign to draft Senator Warren, the Massachusetts Democrat, into the 2016 presidential race, an indication of an appetite among some activists for a more progressive alternative to Hillary Rodham Clinton.

MoveOn.org’s executive director, Ilya Sheyman, said the group planned to open offices and hire staff in Iowa and New Hampshire, the states that kick off the presidential nominating process, and ultimately to air television ads in those states. The group will begin its push with a website, “Run Warren Run,” allowing supporters to sign a petition urging Ms. Warren to pursue a White House bid and featuring a video about her.

“We want to demonstrate to Senator Warren that there’s a groundswell of grass-roots energy nationally and in key states and to demonstrate there’s a path for her,” Mr. Sheyman said. He added that the effort was not being made in coordination with Ms. Warren and that the group advised her staff about it only last weekend.

Ms. Warren, who is entering her third year in the Senate, has fast become a favorite among liberal activists for her unapologetic brand of economic populism, but she has also repeatedly denied any interest in pursuing the presidency.