First Refusal
On February 11, 1953, President Dwight D. Eisenhower denied the petition 
for executive clemency filed by the Rosenbergs. 

These two individuals have been tried and convicted of a most  serious crime against the people of the United States. They have been found guilty of conspiring with intent and reason to believe that it would be to the advantage of a  foreign power, to deliver to the agents of that foreign power certain highly secret atomic  information relating to the national defense of the United States. The nature of the crime for which they have been found guilty and sentenced far exceeds that of the taking of the life of another citizen; it involves the deliberate betrayal of the entire Nation  and could very well result in the death of many, many thousands of innocent citizens. By  their act these two individuals have, in fact, betrayed the cause of freedom for which  free men are fighting and dying at this very hour.
        The courts have provided every opportunity for the submission of evidence bearing on this case. In this time-honored tradition of American justice, a freely selected jury of their fellow citizens considered the evidence in this case and rendered its judgement. All rights of appeal were exercised and the conviction of the trial court was upheld after full judicial review, including that of the highest court in the land*. [bold lettering added] I have made a careful examination into this case, and I am satisfied that the two individuals have been accorded their full measure of justice. There has been neither new evidence nor have there been mitigating circumstances which would justify altering this decision and I have determined that it is my duty, in the interest of the people of the United States, not to set aside the verdict of their representatives.

* Eisenhower's statement is completely false. The Supreme Court never reviewed the case, even though Supreme Court Justices Black, Douglas, and Frankfurter strongly protested the failure to review.  Appellate judges also protested.
 
 
 

Second Refusal
On June 19, 1953, President Dwight D. Eisenhower denied the petition for
executive clemency filed by the Rosenbergs.

Since its original review proceedings in the Rosenberg case by the Supreme Court of the United States, the courts have considered numerous further proceedings challenging the Rosenberg convictions and the sentences imposed. Within the last two days, the Supreme Court, convened in a special session, has again reviewed a further point which one of the justices felt the Rosenbergs should have an opportunity to present. This morning the Supreme Court ruled that there was no substance to this point. I am convinced that the only conclusion to be drawn from a history of this case is that the Rosenbergs have received the benefit of every safeguard which American justice can provide. There is no question in my mind that their original trial and the long series of appeals constitute the fullest measure of justice and due process of law. Throughout the innumerable complications and technicalities of this case, no judge has ever expressed any doubt that they committed most serious acts of espionage*. [bold lettering added] Accordingly, only most extraordinary circumstances would warrant executive intervention in this case. I am not unmindful of the fact that this case has aroused grave concern both here and abroad. In this connection, I can only say that by immeasurably increasing the chances of atomic war the Rosenbergs may have condemned to death tens of millions of innocent people all over the world. The execution of two human beings is a grave matter, but even graver is the thought of the millions of dead whose death may be directly attributable to what these spies have done.
        When democracy's enemies have been judged guilty of a crime as horrible as that of which the Rosenbergs were convicted; when the legal processes of democracy have been marshaled to their maximum strength to protect the lives of convicted spies; when in their most solemn judgment the tribunals of the United States have adjudged them guilty and the sentence just, I will not intervene in this matter.

* Justices Black, Douglas, Frankfurter, Swan and Frank to name but a few who expressed doubts.