Quamaruzzaman, 63, has been convicted of committing crimes against humanity, and siding with Pakistani troops during the Liberation War.
"We greatly respect the decisions of the International Crimes Tribunal and the Appellate Division of the Supreme Court of Bangladesh in Chief Prosecutor vs Muhammad Quamaruzzaman, and note in particular the judicial rigour applied to this ruling," State Department acting spokesperson Marie Harf said.
"We believe that broad and enduring support for this process both nationally and internationally can be best achieved by exercising great care and caution before imposing and implementing a sentence of death," Harf said.
Harf asserted that the ICT trials must be fair and transparent, and in accordance with international obligations that Bangladesh has agreed to uphold through its ratification of international agreements.
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"We have seen progress, but still believe that further improvements to the ICT process could ensure these proceedings meet domestic and international obligations.
"Until these obligations can be consistently met, it is best not to proceed with executions given the irreversibility of a sentence of death," Harf said.
She said countries that impose a death penalty "must do so with great care, in accordance with a very high standard of due process and respect for fair trial guarantees."
If the verdict is carried out, Quamaruzzaman will be the second Jamaat leader after Quader Mollah to be executed for the 1971 offences.