By Shadia Nasralla

VIENNA (Reuters) - A heroin "epidemic" is gripping the United States, where cheap supply has helped push the number of users to a 20-year high, increasing drug-related deaths, the United Nations said on Thursday.

According to the U.N.'s World Drug Report 2016, the number of heroin users in the United States reached around one million in 2014, almost three times as many as in 2003. Heroin-related deaths there have increased five-fold since 2000.

"There is really a huge epidemic (of) heroin in the U.S.," said Angela Me, the chief researcher for the report which was released on Thursday.

"It is the highest definitely in the last 20 years," Me said, adding that the trend was continuing.

The rise could be linked to U.S. legislation introduced in recent years which makes it harder to abuse prescription opioids such as oxicodone, a powerful painkiller that can have similar effects to heroin, Me said.

The law meant the texture of the pills was changed to make it more difficult to crush them and inject them into the blood stream, Me said.

"This has caused a partial shift from the misuse of these prescription opioids to heroin."

Another reason for the increase in the use of heroin, which in the United States mainly comes from Mexico and Colombia, is greater supply that has depressed prices in recent years, Me said.

The United States has also seen a spike in deaths related to fentanyl, a synthetic opioid 50 times stronger than heroin and 100 times more so than morphine, according to the U.S. Centers for Disease Control and Prevention.

Fentanyl has been named as the drug that killed pop singer Prince this year.

At least 207,000 deaths globally were drug-related in 2014, with heroin use and overdose-related deaths increasing sharply also over the last two years, according to the Vienna-based U.N. Office on Drugs and Crime (UNODC).

"Heroin continues to be the drug that kills the most people and this resurgence must be addressed urgently," Yury Fedotov, the executive director of the UNODC, said.

U.S. President Barack Obama earlier this year asked Congress for $1.1 billion in new funding over two years to expand treatment for users of heroin and prescription painkillers.

(Editing by Robin Pomeroy)