WASHINGTON (Reuters) - Influential Republican congressman Paul Ryan disagreed on Sunday with the idea of using the threat of a government shutdown as a means of trying to get rid of President Barack Obama's signature healthcare law known as "Obamacare."

Ryan, chairman of the House Budget Committee and a former vice presidential candidate, said he strongly backs the goal of repealing Obamacare but added there were other, more effective ways of achieving it than by refusing to approve any government funding bill that includes money for the program.

"I think there's going to be a better strategy to actually achieve our goal of ultimately delaying and ultimately replacing Obamacare," the Wisconsin congressman told the CBS talk show "Face the Nation."

Ryan said the shutdown strategy amounted to "swinging for the fences" and wouldn't succeed in gutting Obamacare.

The Republican Party is divided over calls from some conservatives to oppose any annual spending bills that include money for Obamacare. That effort could get in the way of lawmakers' ability to meet an October 1 deadline to pass a funding measure for the federal government. Without such a measure, many government agencies would shut down.

Ryan, author of a Republican budget plan that calls for steep cuts in domestic programs, is considered a possible Republican presidential candidate for 2016.

Republicans have been on a quest to try to kill Obama's 2010 healthcare law, which is due to begin being implemented in October. They argue that it will burden businesses with higher costs and hurt job creation.

Several Republicans who are potential 2016 presidential rivals to Ryan back the shutdown threat, including Texas Senator Ted Cruz, Florida Senator Marco Rubio and Kentucky Senator Rand Paul. But other Republicans view the strategy as reckless and say it's bound to fail.

Ryan said trying to use the annual spending bills as leverage on Obamacare wouldn't work because it is an entitlement program and most of the money for it is not subject to the annual appropriations process.

Even if Republicans were to succeed in withholding so-called "discretionary" spending for Obamacare, the law would live on, Ryan said.

"Rather than sort of swinging for the fences and trying to take this entire law out with discretionary spending, I think there are more effective ways of achieving that goal. We think that we can do better by delaying this law," he said.

(Reporting by Caren Bohan; Editing by Eric Beech)