The four-page document, titled "The Inconvenient Truth", was published on the online message board 8chan about 20 minutes before the shooting.
Chief Allen also released additional information about the shooting, although he said there are many details he couldn't yet disclose.
This weekend's two attacks came less than a week after a 19-year-old gunman killed three people and injured 13 others at the popular Gilroy Garlic Festival in California before dying of a self-inflicted gunshot wound.
The Times also reports that foreign countries have issued warnings in the past noting the presence of mass shootings in the USA, including France, New Zealand and Germany.
This story is breaking and will be updated. Many residents said they believe the warnings are unfair.
Mitch McConnell fractures shoulder after falling in Kentucky home
A group of protesters made some noise outside the home of Senate Majority Leader Mitch McConnell Monday night. The McConnell campaign's tweets on Tuesday suggested that McConnell faced a far greater danger.
Speaking at the White House on Monday, President Donald Trump condemned the two attacks in which 30 people were killed and dozens of others were wounded.
Authorities were investigating the possibility the shooting was a hate crime because of a racist, anti-immigrant screed posted online shortly before the shooting.
In some cases, such alerts have been politically motivated responses to the United States declaring other countries risky, but a growing number of countries have taken America's prevalence of mass gun violence as a serious threat to their citizens. A 21-year-old white male has been arrested.
"The Foreign Ministry warns compatriots traveling to the United States to take precautions against the rise in indiscriminate violence, mostly due to hate crime, including racism and discrimination", the ministry said in the travel alert, which was issued on Monday.
Since 2006, 11 mass shootings - not including Saturday's - have been committed by men who were 21 or younger. In the manifesto, the Texas killer declared that his actions were a form of protecting his country from a foreign "invasion" which he claimed was damaging the culture and economy of the US.
Texas Governor Greg Abbott said Saturday's rampage appeared to be a hate crime and federal prosecutors called it domestic terrorism.