While his fellow Republican presidential aspirants are strongly opposing and urging people to defy the Supreme Court decision legalising same-sex marriages in the United States, Florida Sen. Marco Rubio seemed to have softened his stance on this divisive issue.

In a statement posted on his website, Rubio said while he still advocates traditional marriages between men and women, the Supreme Court ruling giving same-sex couples the right to get married must be followed.

"While I disagree with this decision, we live in a republic and must abide by the law," the Republican senator said.

He nevertheless stressed that marriage is "the most important institution in our society and should be between one man and one woman."

The presidential aspirant also said that individual states should be allowed to enact their own laws on same-sex unions.

"People who disagree with the traditional definition of marriage have the right to change their state laws. That is the right of our people, not the right of the unelected judges or justices of the Supreme Court," Rubio said.

"This decision short-circuits the political process that has been underway on the state level for years," he added.

The senator further said that the issue on gay marriages "is a question of the definition of an institution, not the dignity of a human being."

"Not every American has to agree on every issue, but all of us do have to share our country. A large number of Americans will continue to believe in traditional marriage, and a large number of Americans will be pleased with the Court's decision today. In the years ahead, it is my hope that each side will respect the dignity of the other," he said.

Rubio also urged the next US president to select Supreme Court justices "committed to applying the Constitution as written and originally understood."