"We just had a 'drain the swamp' election," Ryan told members, according to a GOP source in the room. "Let's not just turn around and bring back earmarks two weeks later."
House GOP members applauded and agreed to put off the issue until the first quarter of 2017, when they have more time to have detailed plan to oversee spending bill talks.
Multiple House Republicans told CNN the proposal to reverse the ban was on track to pass in a closed door meeting before Ryan argued to slow down the process.
Supporters of the change argued that ban on earmarks went too far because they can't direct funding to much-needed projects in their districts. They say the shift gave too much power to the White House and unelected bureaucrats in federal agencies who now decide where to spend the money.
Former House Speaker John Boehner ran his leadership campaign on attacking the earmark practice and did away with it when he took over in 2011. Ryan supported that move and has emphasized it in recent speeches.
Arizona GOP Sen. Jeff Flake, a champion of the reform when he served in the House, warned ahead of the vote in a speech on the Senate floor Tuesday that "you can't drain the swamps by feeding the alligators pork."
Idaho GOP Rep. Mike Simpson, a senior member of the Appropriations Committee, told CNN he supported reinstating earmarks but told reporters it would have looked bad for House Republicans to make the change as one of the first moves after the election.
"We shouldn't be the only ones who have to carry this burden. Democrats would just beat the s--- out of us, even though they want to change it as much as we do. So it ought to be done in a bipartisan fashion and I think the speaker made the right decision postponing it."
GOP members told CNN they expected the issue to go through a committee process and eventually a vote on the House floor early next year so that the debate would be out in the open and both parties would be accountable for any change.
That could make it harder for proponents to roll it back since the practice of doling out money with specific line items led to cases of corruption. One former member of the Appropriations panel, California GOP Rep. Duke Cunningham, went to prison over charges that he traded favors for contributions and gifts.
Senate Democratic leader Harry Reid said he strongly opposes the ban on earmarks that was put in place over his objections.
"I'm one of the kinds of earmarks," the retiring Nevadan said. "I think it was a terrible disservice to America to come up with this stupid idea to stop congressional-directed spending."
"I never apologized to anybody," Reid added. "I go home and I boast about earmarks and that's what everyone should do."
But Sen. John Cornyn of Texas, the second-ranking GOP leader in the Senate, said if the rule is changed in the House it's unlikely to be adopted in the Senate and therefore would be moot.
A debate over spending authority
The explosion in earmarks roughly 15 years ago gave the Appropriations Committee the nickname as the "favor factory," with lobbyists contributing campaign donations to members of the panel and clients nabbing federal money for water systems, road construction and other items.
The symbol of some of the wasteful spending was the infamous "Bridge to Nowhere" that linked a small Alaskan town to an island. Construction on that bridge was eventually canceled but it came after a spotlight on the practice of doling out so-called "pork barrel" spending.
"I understand there were problems with it, and there were abuses in the earmark system, but it's still Congress' constitutional duty and responsibility to spend the money," Pennsylvania Republican Rep. Lou Barletta, a member of the Trump transition team, told CNN earlier Wednesday, adding, "some bureaucrat somewhere could be spending this money and now we have no control over that spending."
Barletta said before Ryan's comments that he expected the proposal would have enough votes to pass, but outside conservative advocacy groups were lobbying against it.
Florida Republican Rep. Tom Rooney, one of the members who proposed the change, told reporters Tuesday that the amount of spending wouldn't increase but would just be controlled by members of Congress who know the specific needs of their districts.
Rooney told reporters his proposed change is not about money but about who has the authority to tell the Army Corps of Engineers how to dole out their funds for local projects -- Congress or "unelected bureaucrats."
"I can write a letter and hope that they listen to me, which over at the Army Corps they probably take that letter and put it into the shredder. They don't give a rat's ass what I think."
The proposed rule change, also backed by Rep. John Culbertson and Rep. Mike Rogers of Alabama, would not have opened the door to members directing funds for all agencies, but if it passed it would have certainly put Congress back in charge of who gets billions of dollars in federal money.
Jenny Beth Martin, co-founder of the Tea Party Patriots, pointed to last week's election results as evidence that House Republicans should keep the earmark ban.
"Did they learn nothing at all from these elections? People are tired of business as usual in DC. After this historic election are they really going to go back to business as usual in their first votes? This is not a show of good faith, it's a show of callous cynicism and hypocrisy."
Had the new rule been added to the House Republicans' package that is being crafted this week, it would have gotten a final vote in January when the House approves the guidelines for the new session of Congress.