The survey, conducted by Associated Press and GfK market research firm, came after the Supreme Court ruled on June 26 that same-sex marriage must be legalized at a federal level.
According to the poll, 42 percent favor allowing same-sex couples to be legally married, while 40 percent oppose it.
The number of those approving same-sex marriage decreased by 6 percent from April, while the number of those against it rose by 4 percent over three months.
A total of 39 percent approved the supreme court’s ruling, while 41 percent said they were against it.
Before the Supreme Court decision in June, 37 out of 50 US states and the District of Columbia allowed same-sex marriage.
The poll was conducted between July 9 and 13. A total of 1,004 adults have been interviewed during the poll.