Joseph A. Jakubowski, 32, allegedly robbed the gun shop in Janesville on April 4, the Rock County Sheriff's Office said.
"A large quantity of high-end handguns and rifles were stolen and the suspect fled the scene," authorities said.
About 30 minutes after the burglary, police found Jakubowski's car ablaze on a nearby street along with evidence of arson, according to Cmdr. Troy Knudson.
The suspect was nowhere to be found. Authorities have received nearly 425 tips as they searched for the man.
Some 150 local, state and federal law enforcement officers were actively looking for Jakubowski, the Rock County Sheriff's Office said
. Additional federal officers have been dispatched to the area, officials said Monday.
Authorities said the same day he allegedly robbed the gun shop, Jakubowski sent a 161-page manifesto to Trump.
Knudson said the White House has received the manifesto. CNN has contacted the White House for comment.
It "includes grievances against government and personal angst toward anyone or anything other than natural law or rule," the Rock County Sheriff's Office said.
Authorities released a cellphone video that appears to show Jakubowski at a post office, mailing a bulky envelope addressed to Trump at the White House. The video, which Knudson said was posted on social media, shows Jakubowski's name and a Janesville return address on the envelope.
Knudson declined to confirm what social media platform the video was on.
Investigators said they analyzed the manifesto and discovered anti-religious and anti-government views. As a result, they have beefed up patrols at churches and places of worship, but emphasized that there is no specific threat to any religious group.
"There were two themes in the manifesto," Janesville Police Chief David Moore said. "He was anti-government, and he certainly had his concerns on the federal government, and anti-religion. Those seem to be the two strongest themes."
Services at Bethlehem Lutheran Church in Sun Prairie, near Madison, were canceled Sunday after a man who looked like Jakubowski was spotted near the church on Thursday, the Rock County Sheriff's Office said. Authorities were not able to determine whether the man was Jakubowski.
Knudson said he was unaware of specific people targeted in the manifesto. Rep. Paul Ryan, speaker of the House of Representatives, is a resident of Janesville.
"Local law enforcement was keeping Capitol P.D. in Washington, D.C., abreast of their investigation," Knudsen said.
In the manifesto, Jakubowski also threatened to steal weapons and use them against public officials or schools. Officials put the Janesville School District on a lockdown Thursday and kept schools closed on Friday, according to Janesville School District spokesman Patrick Gasper. School is closed this week for spring break, and students will return April 18.
Gasper said Jakubowski attended Janesville schools during middle school and for his first year of high school. After beginning his sophomore year at Parker High School in Janesville, he left in November 1999 to be home schooled, according to Gasper.
Jakubowski's neighbor Phil Scriven said he saw no signs of trouble in his interactions with Jakubowski, calling him a "pleasant guy."
"Normal guy, normal guy," he said. "He would just sit out here and work on his truck."
Donald McLean, Jakubowski's stepfather, said that while the two are estranged and have not spoken for two years, he hopes Jakubowski will turn himself in peacefully. McLean said around age 17, Jakubowski began hating police and other sources of authority.
"He just generally started hating society, hating police, hating the government, hating rules, regulations, controls, limits," he said.
McLean said he fears if Jakubowski is confronted by police, things could end badly given his feelings toward them and history of fighting with police. His message to Jakubowski is to turn himself in.
"Stop whatever you're doing, whatever you're thinking, put everything down and call 911," he said. "We can start working through the rest of this."
Jakubowski is considered armed and dangerous
. Anyone who sees him should call 911 instead of approaching him, Knudson said.
The FBI has offered a $10,000 reward for information leading to his arrest.
"All local, state and federal agencies continue to be involved in this search and additional resources have come in from Chicago and Minneapolis/St. Paul Minnesota," the Rock County Sheriff's Office said.
Janesville is 70 miles southwest of Milwaukee, near the Illinois border.
It's unclear what Jakubowski's goal is.
"We know he has put a lot of planning into this, we just don't know what the endgame is," Moore said.