(CNN) Nearly one month after the House of Representatives passed sexual harassment legislation to reform the way lawmakers' offices on Capitol Hill handle those cases, Sen. Kirsten Gillibrand is calling out Senate leadership.

"The changes that need to be made are simple and urgent," Gillibrand writes in a letter sent Thursday to Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer, also writing, "The more time that goes by without addressing this broken system, the more people suffer."

The legislation the New York Democrat proposed last year, which has bipartisan support, would overhaul how sexual harassment claims on Capitol Hill are handled. The bill includes removing the requirement that victims undergo mandatory mediation before filing an official complaint. It would also require accused lawmakers to pay settlements with their own money. It aims to boost transparency and will also require members and staff to go through mandatory sexual harassment training every year, and seek to give victims and whistleblowers more support.

Gillibrand wrote, "Something must be done. The House acted, now it is time for the Senate to do its part."

The House passed their version of the bill in early February to reform the Congressional Accountability Act of 1995. Ethics watchdogs, however, say the bipartisan House bill would weaken the authority of the Office of Congressional Ethics, the independent entity currently handling lawmakers' behavior.

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