WASHINGTON (Reuters) - Medicare has become a top healthcare issue in the U.S. presidential election, surpassing the controversy over President Barack Obama's healthcare law, according to a poll conducted just as Republican Mitt Romney pushed the issue to the forefront of the campaign with his choice of running mate.

On Saturday, Romney announced he had picked Representative Paul Ryan, a lawmaker whose plan to cut billions of dollars from the U.S. deficit included transforming the costly, but popular, healthcare program for the elderly.

The nonprofit Kaiser Family Foundation said on Thursday that 73 percent of respondents polled in the days around the announcement described Medicare as "very important" or "extremely important" to their votes. That included large majorities of Democrats, independents and Republicans.

The Kaiser foundation said a separate survey conducted a week earlier found that 58 percent of adults - including 55 percent of Republicans - favored keeping Medicare as it is today with all seniors receiving the same insurance benefits.

Those findings could have implications for Romney and Ryan, and their party, as they battle the Obama campaign over Ryan's plan for Medicare.

Ryan has proposed turning it into a program that provides future retirees with a fixed payment for purchasing private coverage or traditional Medicare, arguing that having seniors manage their own healthcare will help bring down costs.

Critics say the plan would make the elderly responsible for spending thousands more dollars per capita each year on their healthcare.

Only 36 percent of adults - and 39 percent of Republicans - said they favored a plan along the lines proposed by Ryan, according to the July 25-August 5 poll conducted by Kaiser and the Washington Post. That data had a margin of error of 2 percentage points.

In an intensifying war of words, Democrats are attacking the Ryan plan with the claim that it would "end Medicare as we know it." Meanwhile, Republicans accuse the Obama administration of cutting $716 billion from Medicare to pay for "Obamacare," which is unpopular with many voters.

The Kaiser tracking poll, conducted August 7-12, suggests that Obamacare may not hold as much sway with voters as Medicare. The healthcare reform law ranked fifth as a healthcare issue, with 59 percent of adults calling it "very" or "extremely" important.

Medicare shared the top ranking among campaign healthcare issues with medical costs, including the price of health insurance, the poll showed.

About half the respondents said they lacked a basic understanding of Romney's policies on healthcare. But 53 percent said they trusted Obama to make the right decisions about the future of the healthcare reform law, versus 40 percent who said they trusted Romney.

The Kaiser tracking poll has a 3 percentage point sampling error.