HARTFORD, Conn. — Connecticut moved a step closer Tuesday to setting up a new health insurance marketplace, backing legislation in the state Senate establishing a health insurance exchange called for by federal law.

The Democratic-led Senate approved the measure 23-13 with near-unanimous opposition by Republicans. The legislation establishing the Connecticut Health Insurance Exchange, a quasi-public agency, now heads to the House of Representatives for debate.

A 14-member board would manage the exchange, including an online marketplace where individuals and employers with up to 50 workers can compare and purchase health insurance plans that, starting in 2014, meet federal requirements.

The aim is to bring down prices and get more people insured. The exchanges are set to open for business in 2014.

The Connecticut exchange would certify, recertify and decertify health benefit plans, provide enrollment periods, maintain a website offering standardized comparative information on health plans, and screen applications to determine eligibility for Medicaid, the state Children’s Health Insurance Program or other state public insurance programs and enroll eligible applicants.

Several other states are setting up the exchanges, with some legislatures meeting resistance from conservatives who opposed the federal health care legislation enacted in March 2010 by the Democratic-led Congress and President Obama.