Federal officials are examining the mysterious incident that left Martinez, 36, dead and his partner battered and unable to remember what happened.
US Attorney General Jeff Sessions and other law enforcement officials were scheduled to attend the private service at the Our Lady of Guadalupe Catholic Church in El Paso, Texas.
The city's iconic landmark Star on the Mountain
-- a man-made illuminated star on the side of the Franklin Mountains --- will be lit over the weekend in honor of Martinez, CNN affiliate KFOX
"Roger, our beloved friend, son, father and dedicated agent. We will miss you dearly. Tonight we light up the star in your honor. We love you, our hero," a certificate about the lightning of the star read.
The American flag flew at half-staff at the Department of Homeland Security headquarters Friday to honor Martinez, DHS tweeted.
Martinez's partner, who has not been identified, was released from the hospital this week and is walking on his own with a cane, said Lee Smith, the region's chapter president of the Border Patrol union.
The agent doesn't recall what happened and says the last thing he remembers is arriving at work that night, Smith said.
Both men had been on patrol near Interstate 10 in the Big Bend Sector, which runs along the US-Mexico border, when they responded to what border officials described as "activity."
After they responded to the call, Martinez's partner reported that they were both injured and needed help, according to CBP.
They were found in a culvert area -- a tunnel structure used for water drainage -- 12 miles east of the town of Van Horn at 11:20 p.m. Saturday, the FBI said.
The FBI said the men suffered traumatic head injuries and other wounds such as broken bones.
Martinez died from his injuries at a hospital Sunday morning. His partner was in serious condition when he was taken to the hospital, but was released within a few days.
The results of Martinez's autopsy are pending.
Part of the agents' regular duties include checking culverts off the interstate for undocumented immigrants, said Rush Carter, the special operations supervisor for the Big Bend Sector of the US Border Patrol.
Chris Cabrera, the National Border Patrol Council spokesman, described the incident as an "ambush" and suggested that drug traffickers frequented the area.
"It was a brutal attack," Cabrera said. "This was something well thought out and planned. They executed their plan."
Texas Gov. Greg Abbott's office has authorized a reward of up to $20,000
for information leading to the arrest of those responsible.