The proposal was blocked by Republican Sen. Cindy Hyde-Smith of Mississippi, who argued that the law should not be "exempt from consideration by the appropriate jurisdictional committee".
"Legislation affecting the rights of US citizens under the Second Amendment should not be followed quickly by the Senate," Hyde-Smith said Thursday.
"If this so-called bipartisan common sense legislation was really done with strong bipartisan input, there should be no problems moving forward on a regular basis, "she added. "Many questions about this legislation need to be answered before the law-abiding gun owners are forced."
Following Hyde-Smith's action, Murphy said, "I cannot get floor legislation in any other way than to offer this movement," Murphy said, citing Republican control of the committee. "And the American public will not accept silence from this body week after week, month after month, before this epidemic massacre is taking place across the country."
Adopted by the United States House of Representatives in February, the 8th RD will have to carry out background checks on all firearms sales in the country. Currently, under federal law, only licensed arms dealers must carry out background checks for anyone who wants to buy firearms, which leaves weapons sales among individuals largely unregulated.
The report was also contributed by CNN's Caroline Kelly and Claire Foran.