By Deena Beasley and Toni Clarke

LOS ANGELES/WASHINGTON (Reuters) - Americans' growing alarm over rising prescription drug costs will pressure a new U.S. administration and Congress to take action on pharmaceutical pricing, industry executives and healthcare experts say.

Drugmaker stocks, battered in recent months, soared this week after Republican presidential candidate Donald Trump's victory. Democratic rival Hillary Clinton had vowed to take on pharmaceutical "price gouging," and some pundits predicted the Democrats would gain control of the Senate, giving her a stronger hand.

The Republican sweep of Congress eliminated those fears, while boosting chances for other measures, such as corporate tax reforms that would benefit industry.

However, the vote did not change a key dynamic: U.S. consumers are paying more of the cost of drugs through higher health insurance deductibles and copayments, making them more sensitive to manufacturer price hikes.

Most recently, a sixfold increase in the price of Mylan NV's EpiPen stoked outrage for families who rely on the lifesaving allergy shot and prompted investigations by state attorneys general and Congress.

If a manufacturer sharply raises the price of a drug, "it will be in the headlines. I don't think it matters which party is in office," said Sandra Hunt, principal at PricewaterhouseCooper's health industry practice.

Republican lawmakers have taken up drug pricing alongside Democrats. Republicans Senator Charles Grassley of Iowa, chair of the Senate Judiciary Committee, and Representative Jason Chaffetz, chair of the House Committee on Oversight and Government Reform, led inquiries into Mylan's EpiPen pricing.

"A very strong majority of Republican voters want the Congress to address drug prices," said John Rother, president and CEO of the National Coalition on Health Care, which campaigns for lower prices.

An October Kaiser Family Foundation survey showed that 74 percent of respondents said making drugs for chronic conditions affordable should be a top health care priority for the federal government. Among Republican respondents, 68 percent put drug prices as a top priority.

A poll conducted by the Harvard T.H. Chan School of Public Health found that 64 percent of voters - including 78 percent of likely Clinton voters and 48 percent of Trump supporters - believe the federal government should be able to limit pharmaceutical drug price hikes.

BIGGER PRIORITY THAN OBAMACARE

Trump and Republican leaders have vowed to repeal President Barack Obama's healthcare reform law, known as Obamacare, which has extended medical insurance to more than 20 million Americans. Despite complaints about Obamacare insurance premium increases, just 37 percent of Kaiser poll respondents said that overturning it was a high priority.

Chaffetz is "evaluating his next steps" on the drug pricing issue when the next Congress convenes, an aide said. A representative for Grassley said he would press forward with a scheduled Nov. 30 hearing into Mylan's EpiPen pricing.

"The U.S. has always been a country that supports innovation ... and we hope it will remain the same," said Pascal Soriot, chief executive of AstraZeneca Plc, which sells drugs like cholesterol-fighter Crestor. "But we also believe we will continue to have to deal with price ressures."

Clinton's proposals to curb drug prices included capping consumers' monthly out-of-pocket costs. In the past, Trump has suggested allowing the government's Medicare health program for seniors to negotiate prices and making it easier to import drugs from countries where they sell for less.

A Trump administration also could provide extra funding to the U.S. Food and Drug Administration to speed approval of generic drugs, which still tend to cost far less than their brand name equivalents, health policy experts said.

Capital Alpha Partners analyst Kim Monk, in a research note on Wednesday, said she expects advisors and Congress to steer Trump toward "more Republican-oriented ideas," including pricing drugs based on their relative health benefit and requiring more disclosure of pricing details.

Consumer advocate Rother cited the FAIR Drug Pricing Act, introduced in September by Senators John McCain, an Arizona Republican, and Tammy Baldwin, Wisconsin Democrat, as a potential vehicle for federal action. The bill would require manufacturers to explain annual price increases of more than 10 percent.

"It is a bipartisan bill consistent with traditional Republican health policy based on transparency and competition," Rother said.

In California, voters on Tuesday rejected a ballot measure that would have require drugmakers to provide state health plans with discounts similar to those given to the U.S. Department of Veterans Affairs. The VA pays the lowest prices in the country.

Drugmakers spent more than $106 million on a campaign to defeat the measure.

A similar measure will go before Ohio voters, who backed Trump in the election, next November. The coalition behind California's proposition on Wednesday urged legislators to come up with "a more comprehensive solution to lower sky-rocketing drug prices."

(Reporting by Deena Beasley in Los Angeles and Toni Clarke in Washington; Editing by Michele Gershberg and Lisa Girion)