Cabinet minister Andrew Robb says same-sex marriage is a "20th order" issue and the government can't afford to be distracted by the debate.
The trade minister's comments came as cabinet colleague Christopher Pyne rejected calls for ministers to resign if they support the law change.
Mr Robb told ABC radio on Friday the issue could end up distracting the government for months, losing many days of debate on economic management and national security.
"It is important to a lot of people, but for most people it's a 20th-order issue, and we've got to look at the priorities for the community," he said.
"This should not be allowed to distract us from the key priorities that we've got."
Workplace Minister Eric Abetz has said Liberal Party policy was for male-female marriage only and if frontbenchers want to cross the floor in parliament they should resign first.
But Mr Pyne said calls for resignations were "not helpful".
"He (Senator Abetz) should express his conscience however he likes to express it. There are others within the party with a different view and they also need to be respected," he told the Nine Network.
Deputy Prime Minister and Nationals leader Warren Truss said roads and economic development were more important than changing the Marriage Act.
"Ultimately it's for members of parliament to vote on issues that come before the parliament," he told reporters in Brisbane.
"But from my perspective there are more important things to be dealt with. That includes selling a big budget with items that are of enormous benefit - we need to keep the economy strong."
Liberal MP Warren Entsch is proposing to take a same-sex marriage private member's bill to parliament in August, seconded by Labor MP Terri Butler.
Labor frontbencher Anthony Albanese said Prime Minister Tony Abbott should allow all Liberal MPs a free vote and the bill should be voted on in the second half of the year.
"I suspect when it does, it will be carried and we'll all move on," Mr Albanese said.
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