"I support traditional marriage," Cruz said in a release announcing introduction of the bill Wednesday. "We should respect the states, and the definition of marriage should be left to democratically elected legislatures, not dictated from Washington. This bill will safeguard the ability of states to preserve traditional marriage for its residents."
The State Marriage Defense Act would ensure the federal government offers the same deference to the 33 states that ban same-sex marriages as it does to the 17 states that allow them, he said.
"How a state should define marriage should be left up to the citizens of each state," Lee said. "The State Marriage Defense Act provides an important protection for states, respecting the right to choose for themselves how each will treat the institution of marriage under the law."
Months after the U.S. Supreme Court struck down a federal ban on recognizing same-sex marriage, the Justice Department said that the federal government would treat same-sex marriages the same as it does heterosexual marriages.
A similar State Marriage Defense Act was introduced in the U.S. House in January by Rep. Randy Weber, R-Texas.
Family Research Council President Tony Perkins said his organization was pleased that Cruz and Lee were "stepping in to make sure the federal government respects state marriage laws."