The President's eldest son, Donald Trump Jr, took aim at leaders in his own party for failing to take "action" while the votes are counted.
In another tweet, he said his father should go "to total war" over the election.
Eric Trump has also jumped in, pleading with Republicans to "have some backbone" instead of being "sheep".
While some Republicans have supported Trump's baseless claims of electoral fraud, others have remained silent.
Some Republicans appear to be responding by showing support for Trump's legal challenges and praising the President for his leadership.
A number of key battleground states have yet to be decided and the winner of the election has not been declared.