The list, which also includes preventing immigrants from sponsoring their extended families to move to the US.
The list, which also includes preventing immigrants from sponsoring their extended families to move to the US, drew immediate fire from Democratic leaders in Congress, who said it goes "far beyond what is reasonable."
The administration tied its priorities to Democrats' desire to provide legal protection to some 690,000 immigrants known as "Dreamers" who came to the country illegally as children and were covered by an amnesty by former president Barack Obama that Trump scrapped last month.
"These findings outline reforms that must be included as part of any legislation addressing the status of Deferred Action for Childhood Arrivals (DACA) recipients," Trump wrote in a letter to Congress accompanying the list, using the official name for the amnesty order.
The White House list is topped by "border security," a category that includes building a massive wall on the southern US border that Trump promised would be paid for by Mexico, which has said it will not do so.
Trump also wants to dramatically ramp up the number of officials involved in enforcement, hiring an additional 10,000 Immigrations and Customs Enforcement officers and 1,000 attorneys, 370 immigration judges and 300 federal prosecutors.
And he hopes to prevent immigrants from sponsoring extended family members to move to the US, limiting such green cards to spouses and children, as well as to close "loopholes" that prevent the deportation of children who enter the country illegally.
The list includes financially targeting "sanctuary cities" that have resisted the Trump administration's efforts to crack down on illegal immigrants.
"The administration proposes blocking sanctuary cities from receiving certain grants or cooperative agreements administered or awarded by the Departments of Justice and Homeland Security," it said.
Other proposals include cracking down on people who overstay visas, restricting asylum and expanding criteria that would make someone inadmissible to the US.
Trump's list was criticized by Chuck Schumer and Nancy Pelosi, the respective Democratic leaders in the Senate and House.
"This proposal fails to represent any attempt at compromise," the legislators said in a joint statement.
"The list includes the wall, which was explicitly ruled out of the negotiations. If the president was serious about protecting the Dreamers, his staff has not made a good faith effort to do so."
The president has previously insisted the wall will go ahead and that he wants "massive border security" in exchange for a deal on DACA protections.
Trump has made toughening immigration regulations a central part of his first year in office, also issuing several versions of a controversial travel ban that has been criticized for targeting Muslim-majority countries and subject to numerous legal challenges.
The latest version, which was unveiled last month, bans citizens of Chad, Iran, Libya, North Korea, Somalia, Syria and Yemen from entering the US.
Also suspended are certain Venezuelan government officials and their families, due to what the US called poor security and a lack of cooperation with American authorities.