Sen. Gillibrand, D-N.Y., told the "Fox News Rundown" podcast health care, immigration reform and connecting with voters are other top concerns in her bid for the White House. She also discussed her upcoming Fox News town hall this weekend.
"I've been working on these issues for over a decade," Gillibrand told host Dave Anthony. "I've been leading on issues of gender equality and valuing women since I've been in the House and the Senate."
The New York Democrat said she worked on paid-leave legislation while serving in Congress.
"It's really important that we know that men and women in the workplace can have that flexibility when they need it to deal with an urgent crisis," she said.
Gillibrand cited potential cases of an employee with a sick or elderly parent or a parent who requires maternity leave as situations other nations have addressed at the federal level.
"We're the only industrialized nation country in the world that doesn't have access to paid leave."
She added if the federal government concentrated on such policy changes, "all of our workers can work at their fullest economic potential to keep our economy strong."
Gillibrand charged presidential candidates like herself who are not "front-runners" in the primary contest must build their support from the grassroots.
"In historic terms, front-runners today are not the winners tomorrow. So, you need to earn support one voter at a time [or] one caucus-goer at a time. I think I could do that."