Trump had told reporters at the White House that Herzog was "disgraceful" and should be "ashamed of himself" for not yet pardoning the Israeli Prime Minister Benjamin Netanyahu, who is accused of corruption.
Trump said Netanyahu had achieved extraordinary things during wartime.
The office of the Israeli president then clarified that Herzog had not yet made a decision regarding the pardon, contrary to Trump's portrayal.
The application, which Netanyahu submitted in November, is still being reviewed by the Ministry of Justice, according to established procedures, it said.
Only after the completion of this process will Herzog consider the application "in accordance with the law, in the best interest of the State of Israel, guided by his conscience and without any external or internal pressure," his office further stated.
Herzog deeply appreciates Trump for his support of the Jewish state, but Israel is a sovereign state governed by the principle of the rule of law, his office said.
Shortly before Trump's attack on Herzog, the US president had met Netanyahu at the White House.
According to media reports, Herzog's office has therefore demanded explanations as to whether Netanyahu encouraged Trump in his remarks against the Israeli president.
Sources close to Netanyahu stated that Trump's demand for a pardon was solely on the initiative of the US president himself.
"The prime minister learnt about it from the media and knew nothing about it in advance," they stated.
Netanyahu had officially requested a pardon from Herzog in a letter.
It is unclear when Herzog will make a decision on this matter.
Netanyahu has been undergoing a corruption trial for more than five years.
He is charged with fraud, breach of trust and bribery.
Trump has repeatedly urged Herzog to pardon Netanyahu.
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