Several executions were delayed after a judge ruled on Monday that there were still unresolved legal challenges against the justice department.
Among those facing the death penalty is triple murderer Daniel Lewis Lee, who was due to be executed on Monday.
The condemned prisoners have argued that lethal injections constitute "cruel and unusual punishments".
The Supreme Court voted 5-4 that "executions may proceed as planned".
Last year, the Trump administration said it would resume federal executions.
In a statement at the time, Attorney General William Barr said: "The justice department upholds the rule of law - and we owe it to the victims and their families to carry forward the sentence imposed by our justice system."
Some of the relatives of Lee's victims oppose his execution in Indiana and had sought to have it delayed, arguing that attending it could expose them to coronavirus.
Earlene Peterson, 81, whose daughter, granddaughter and son-in-law were killed by Lee, has said she wants the 47-year-old to be given life in jail, the same sentence as his accomplice.
The Trump administration's move has been criticised as a political decision, with campaigners expressing concern about cases being rushed.
The last inmate executed by federal death penalty was Louis Jones Jr, a 53-year-old Gulf War veteran who murdered 19-year-old soldier Tracie Joy McBride.
Federal and state executions - what's the difference?
Under the US justice system, crimes can be tried either in federal courts - at a national level - or in state courts, at a regional level.
Certain crimes, such as counterfeiting currency or mail theft, are automatically tried at a federal level, as are cases in which the US is a party or those which involve constitutional violations. Others can be tried in federal courts based on the severity of the crimes.
The death penalty was outlawed at state and federal level by a 1972 Supreme Court decision that cancelled all existing death penalty statutes.
A 1976 Supreme Court decision allowed states to reinstate the death penalty and in 1988 the government passed legislation that made it available again at federal level.
According to data collected by the Death Penalty Information Center, 78 people were sentenced to death in federal cases between 1988 and 2018 but only three were executed. There are 62 inmates currently on federal death row. BBC