The execution of a Mexican national, Edgar Tamayo, in Texas were put on hold on Wednesday as the the US supreme court considered appeals.

There have been international protests at the planned exectuion and amid fresh scrutiny of the methods states are using to carry out lethal injections.

Dennis McGuire was executed in Ohio last Thursday using a new two-drug protocol, and eyewitness accounts suggested that he suffered an agonising death that took up to 25 minutes. Edgar Tamayo will be put to death in Texas using pentobarbital bought from a compounding pharmacy, a method the state introduced last autumn. Prison officials revealed to the Associated Press last October that they started using compounded pentobarbital after the state's previous supply of the drug expired.

States have turned to compounding pharmacies and single-drug protocols in recent years after running out of their usual stocks because of a boycott by European pharmaceutical companies. But lawyers for death row inmates have repeatedly – though largely without success – challenged the use of such drugs, claiming they could cause undue suffering.

Compounding pharmacies custom-make or blend drugs and are typically regulated at state level , which has led to fears of a lack of transparency and lax oversight. They need not register with the Food and Drug Administration (FDA) and are not necessarily subject to the federal body's rules. The government tightened regulations for large-scale compound companies after tainted steroids from a pharmacy near Boston in 2012 caused a meningitis outbreak that killed 64 people.

Three inmates on Texas death row filed an unsuccessful lawsuit last October alleging that the use of non-FDA-approved pentobarbital was potentially a cruel and unusual punishment that would violate their constitutional rights. Texas, home to the nation's busiest death chamber, has executed five prisoners since September. It began using a single-drug method in July, 2012. Pentobarbital is an anaesthetic commonly used to euthanise animals.

After The Woodlands Compounding Pharmacy near Houston was revealed as the new source of the drug, it sent a letter to the Texas department of criminal justice demanding the vials be returned because the owner said he had been promised secrecy. The state refused to comply.

Three Texas executions have been carried out using compounded pentobarbital, according to Jason Clark, a spokesman for the Texas Department of Criminal Justice. "The quality and potency of the compounded pentobarbital does not differ from the pentobarbital that is manufactured by a pharmaceutical company," he said. Clark declined to comment on the size of Texas's supply and whether it holds stocks of any other drugs.

Tamayo had been scheduled to be executed at 6pm central time for the fatal shooting of Guy Gaddis, a Houston police officer, in 1994. His lawyers argue that the 46-year-old did not receive a fair trial because he was denied prompt consular assistance, in violation of the Vienna Convention.

It was postponed as the supreme court deliberated, with the execution warrant due to expire at midnight.

On Tuesday a federal judge in Austin refused Tamayo's request for a restraining order to stop governor Rick Perry and the Texas board of pardons and paroles from considering Tamayo's clemency petition until the procedure is "adequate and fair".

His lawyers claim that he is mentally disabled and that timely consular assistance could have helped him avoid the death penalty. They also contend that Perry and Greg Abbott, the Texas attorney general, have failed to keep a promise to provide a specific review of the impact of Tamayo's loss of consular rights, as was mandated in a 2004 judgment by the International Court of Justice.

In 2008, the supreme court ruled that in the absence of a statute from Congress, Texas was not obliged to obey President George W Bush's instruction that states should comply with the international court's ruling. Texas officials have argued that Tamayo's conviction and the appeals process were fair.

The case has garnered a great deal of media attention in Mexico, and officials including the country's foreign minister and ambassador to the US have urged Texas to halt the execution, as have several human rights groups and Mark White, a former Texas governor. John Kerry, the US secretary of state, sent a letter to Perry last September warning that the failure to respect international law could damage relations with Mexico and make foreign countries less inclined to respect due process for Americans abroad who find themselves in legal trouble.

Tamayo's lawyers said in a statement:

It is widely known that the Texas clemency process is the weakest in the nation, in the state that executes the most. Allowing Mr Tamayo’s fate to be decided by a board that has refused to provide meaningful consideration of evidence that Mr Tamayo has mental retardation and that his trial was fundamentally unfair as a result of the violation of his consular rights, is an affront to what clemency is supposed to be, a 'failsafe' in our justice system.

His lawyers said on Wednesday morning that they would continue to fight the execution through the legal system until the last possible moment.