Louisiana Governor and Republican presidential hopeful Bobby Jindal has signed a law that would provide state residents access to medical marijuana, more than two decades after the state allowed the chronically ill to use cannabis, officials said.

The law forms part of a program where the drug will be legally cultured and distributed. It filled a crucial gap in the legislation on medical marijuana that was green-lit by the state in 1991, The Huffington Post wrote.

Louisiana is now the first Southern US state to make the drug accessible to its residents for medical use, joining the ranks of the District of Columbia and 23 other states where medical marijuana is already legal and available.

The governor also signed a law reducing second-time pot possession to a misdemeanour from a felony. The measure also allows first-time offenders to strike out their conviction after two years if they do not possess marijuana again.

"Louisiana's overdue for a major overhaul of its drug policies and this is a good first step," said Yolande Cadore of the Drug Policy Alliance. "It's a relief to see that smart policymakers are starting to recognise this political reality."

However, it would take at least two years before the drug can be obtained by those with medical prescription following the extensive regulatory process to select and supervise a state-authorised grower as well as 10 licensed distributors, The Washington Times reported.

In a Pew survey in March, 59 percent of Americans disapprove federal government intervention in states where marijuana is legal. The figure includes 54 percent of Republicans. Meanwhile, 53 percent of Americans back the legalisation of marijuana.

Following the green-lighting of measures on medical marijuana, Jindal became the latest Republican presidential candidate to espouse a drug policy reform. Senator Rand Paul pushes for a measure shielding states that legalise medical marijuana from federal interference and allowing marijuana firms to use the banking system.

Ex-Texas Gov. Rick Perry, on the other hand, said he would respect the right of states to craft their own marijuana laws.