Mr Trump said in a written statement on Sunday that pulling all US troops from Afghanistan was "a wonderful and positive thing to do".
However he complained the new administration’s target missed the 1 May deadline formerly agreed between Mr Trump’s negotiators and the Taliban.
The former US president wrote that "we should keep as close to that schedule as possible” and that the withdrawal should be sooner than September out of respect for US forces.
"I wish Joe Biden wouldn't use September 11 as the date to withdraw our troops from Afghanistan,” said Mr Trump, “for two reasons.”
“First, we can and should get out earlier. Nineteen years is enough, in fact, far too much and way too long,” Mr Trump said in the statement, first reported by Axios.
The former president continued by saying that "September 11 represents a very sad event and period for our country and should remain a day of reflection and remembrance honouring those great souls we lost”.
Mr Trump, a critic of the conflict, once called Afghanistan “a complete waste”, and tweeted in 2013 that the US “should leave Afghanistan immediately”.
Ally and Republican senator for South Carolina, Lindsey Graham, wrote on Sunday that he “could not disagree more” with the former president’s remarks.
Mr Biden on Wednesday said all of the country’s remaining forces in Afghanistan would start withdrawing from 1 May, and before 11 September – the 20th anniversary of the terror attacks that triggered the war in 2001.
"It was never meant to be a multi-generational undertaking,” said Mr Biden of the plans to withdraw, which he said were in line with the Trump agreement with Afghan forces and the Taliban.
“We were attacked. We went to war with clear goals. We achieved those objectives,” Mr Biden added, "and it's time to end the forever war.”
A number of troops will remain in the country for the protection of US diplomats and officials after an estimated 2,500 to 3,500 troops depart.
Additional reporting by Reuters