The US state of Georgia has hurriedly executed Andrew Allen Cook amid a legal scramble to carry out capital sentences before its supply of lethal injection drugs reaches its expiry date of 1 March.

Cook, 38, had been on death row for the killing of two college students in 1995.

The Georgia appeals court on Wednesday temporarily stayed Cook's execution to consider a challenge to the state's lethal injection procedure. But the Georgia supreme court lifted the stay on Thursday. Other appeals were exhausted.

Cook was the first inmate to be executed since the state changed its execution procedure in July from a three-drug combination to a single dose of the sedative pentobarbital.

Georgia is also pushing to execute Warren Hill, who has been diagnosed as intellectually disabled, before 1 March. Hill's death warrant runs until 26 February and Cook's had been due to run out on 28 February.

The attorney general of Georgia – the state's chief prosecutor – is hurriedly trying to have Hill's stays of execution overturned. The courts intervened after it was found that pentobarbital was being ordered by the corrections department for use as a lethal injection without a prescription from a doctor – a breach of federal rules over the distribution of a controlled substance.

The attempt to execute Hill has provoked international condemnation because of his disability. A federal appeals court has also blocked the execution to allow time to consider the disability issue, and on Thursday the US supreme court denied Georgia's request to overturn the stay.

Warren Hill.

Georgia confirmed to the Guardian that its entire supply of pentobarbital expires on 1 March. The expiration date leaves the state in a quandary: it still has 93 men and one woman on death row, including Hill, but with no obvious means by which to execute them.

A spokeswoman for the department of corrections insisted that it anticipated "it will be able to obtain sufficient supplies of the drugs necessary to carry out the court ordered lethal injection process." But just how that could be done is not obvious.

Anti-death penalty campaigners are scathing about the unseemly haste with which Georgia appears to rushing to beat the deadline. "This highlights the nastiness of the process that the AG should be racing to kill prisoners ahead of an expiration date," said Sara Totonchi, director of the Southern Center for Human Rights.

Georgia's difficulties procuring execution drugs is a reflection of the gradual stranglehold that is being put on the US death penalty by authorities and companies around the world refusing to act as accomplices in the death sentence. The European commission, following unilateral action by the UK, has imposed restrictions on the export of medicines to all US corrections departments.

As a result of the European squeeze, Hospira, the only US manufacturer of sodium thiopental, an anaesthetic that was used widely in the triple cocktail of lethal injections, ceased production in 2011. That, in turn, forced states including Georgia to revise their death protocols, shifting to a single injection of pentobarbital.

But now supplies of pentobarbital are also running out. One of the leading manufacturers of the drug, the Danish firm Lundbeck, has introduced tough restrictions on the distribution of the drug to prevent it falling into the hands of US executioners.

As legal routes for the procurement of medical drugs have been successively shut down, several of the 33 states that still practice the death penalty have resorted to shady methods for acquiring them. Georgia was exposed in 2011 as having been one of the states that bought lethal injection drugs from Dream Pharma, an unlicensed company that operated out of a driving school in west London.

Other corrections departments have looked to India for their supplies.

Maya Foa, an expert on execution drugs at the human rights group Reprieve, said that at the heart of the issue was a fundamental principle "that medicines should be used to save lives, not end them. The underhand, sordid practices we have seen in states trying to get hold of these drugs exposes their absolute disregard for human dignity."

As Georgia struggles to find new sources of pentobarbital or alternatives, death penalty abolitionists will be watching closely for any signs that they are turning to compounding pharmacies to make up the drugs for them. In October, South Dakota executed Eric Robert using a batch of pentobarbital that it had obtained from a local pharmacy.

Tests that were done on the batch showed that it was contaminated with fungus, in an echo of the 2012 outbreak of fungal meningitis that was tracked down to a compounding centre in Massachusetts.