"We're on the right path,'' Villanueva said Tuesday. He also expressed hope to have something to announce soon.
Investigators were "working day and night to identify and arrest these cowards,'' Villanueva said, referencing the gunman and a possible getaway driver.
RELATED: Video shows wounded deputy struggle to aid partner after Compton shooting
As of Wednesday morning, no suspects had been identified, despite some online social media chatter to the contrary.
The sheriff's department issued a statement early Monday saying the information circulating online "is ERRONEOUS information and there are no named or wanted suspects at this time.''
A GoFundMe page set up for the two deputies exceeded its original goal of raising $400,000 as of Wednesday morning. As of 8 a.m., more than 7,600 people had donated over $513,000 toward the page's new goal of $750,000. The page, started by sheriff's detective Keegan McInnis, can be found here.
The deputies remained hospitalized in stable condition following surgery for their wounds.
"Fortunately, they were spared any injury to a vital organ that would have jeopardized their life immediately,'' Villanueva told KNX-AM on Monday.
But the sheriff said the deputies -- described only as a 24-year-old man and a 31-year-old mother of a 6-year-old boy -- have a long road to recovery. Villanueva said Saturday both deputies were sworn in just 14 months ago.
Villanueva challenged Lakers star LeBron James, who has been outspoken on social-justice issues and in support of the Black Lives Matter movement, to match the reward offer.
RELATED: Sheriff Villanueva challenges LeBron James to match reward money for Compton shooting gunman
Villanueva said Tuesday that he singled out James because of the player's previous comments after last month's police shooting of Jacob Blake in Kenosha, Wisconsin.
"He symbolized some of the comments we've heard from politicians, elected leaders, civic leaders, where they're making a broad-brush condemnation of an entire profession,'' Villanueva said.
"I just think we need to put down the broad brushes and re-focus on all the people accountable when they cross the line, as we are doing with law enforcement across the entire nation.''
James has not responded to Villanueva's comments.
The Board of Supervisors formally ratified a $100,000 reward offer Tuesday. Villanueva, speaking at the outset of the board meeting, said the reward had "now been matched and exceeded by private donors.''
The Los Angeles County Metropolitan Transportation Authority announced Monday afternoon it was adding $25,000 to the reward, noting that the deputies were working for Metro's Transit Services Bureau at the time of the shooting.
The League of United Latin American Citizens added another $25,000 to the reward money, and the Association for Los Angeles Deputy Sheriffs, the union that represents the department's deputies, announced Tuesday night that it was donating $75,000.
Members of the county board said cities including Palmdale, Cerritos, Lakewood and Industry had also added to the reward, though the totals were not immediately available.
Supervisors Kathryn Barger and Mark Ridley-Thomas authored the reward motion.
Barger said she had visited St. Francis Medical Center in Lynwood and saw deputies in the waiting room who were "deflated but not deterred.'' Then she went to the command post.
"I looked around. There were about 80 deputies who mirrored the communities that they are working in. These are people that, for the most part, are from these communities who want to protect their communities. So while this ambush truly was heinous, what it has shown me is that we have people that take an oath to protect our communities even under the threat of maybe not coming home to their families,'' Barger said, her voice shaking.
"And so I hope that we will remember that and hold them and their families and each and every single sheriff's deputy, each and every law enforcement (officer)... in our thoughts and prayers during this difficult time.''
Ridley-Thomas urged those who know the gunman to contact the Sheriff's Department's Homicide Bureau at 323-890-5500. Anonymous tips can be left for L.A. Crime Stoppers at 800-222-TIPS (8477), or at http://lacrimestoppers.org.
"We simply cannot tolerate this kind of lawlessness,'' he said.
Supervisor Janice Hahn also pushed anyone with information to come forward.
"Somebody knows who this person is, they know their name and we're hoping that this will bring that information forward so we can bring this perpetrator to justice,'' Hahn said.
SHOOTING AND AFTERMATH
The attack occurred at 7 p.m. Saturday at the Metro Blue Line station at Willowbrook Avenue and Palmer Street. Surveillance video shows the suspect approaching the window on the passenger's side and firing several times at close range. The suspect then ran off on foot. One deputy was seen emerging from the passenger side and stumbling around on foot for several seconds before the video ends.
Audio captures a frantic call for help from one of the deputies shortly after the shooting.
"I've been shot. Send help," one of the deputies is heard saying in the radio call.
Shortly after the shooting, the female deputy can be seen on surveillance video struggling to place a tourniquet on her partner even as she herself is bleeding from gunshot wounds.
"She helped the other wounded deputy, got on the radio, provided medical care, got him to a place of safety 'cause they didn't know if there was another attack coming their way," Villanueva said.
The shooter was described by the sheriff's department as a "male Black, 28- to 30-years-old, wearing dark clothing, who was last seen heading northbound on Willowbrook Avenue in a black four-door sedan.''
Relatives of the injured deputies -- including the husband of the female deputy and the girlfriend and parents of the male deputy -- were at St. Francis Medical Center in Lynwood, where they're being treated.
Villanueva on Monday again lashed out at protesters who showed up at the hospital Saturday night and shouted anti-law-enforcement chants, expressing hope that the deputies die. One witness told ABC7 some protesters tried to force their way into the emergency room while shouting death to the police.''
"They were chanting that they wish the deputies died,'' Villanueva told KNX Monday. And I don't even know how to be begin to describe that, other than repulsive, reprehensible.''
More video surfaced Monday showing some bystanders at the Metro station taking pictures or video of the wounded deputies after the shooting, and at least in one case, laughing while failing to offer any kind of aid.
WATCH: Protesters show up to hospital after Compton deputy shooting
County Supervisor Kathryn Barger didn't mince words Monday about her disgust with the hospital protests. She suggested the shooting was the culmination of "anti-law-enforcement rhetoric expressed by many elected officials, community leaders and others,'' leading to the creation of a toxic environment amid a time of civil unrest.''
The shooting came on the heels of a series of combative protests outside the sheriff's South Los Angeles station, with demonstrators condemning the Aug. 31 fatal shooting by two sheriff's deputies of 29-year-old Dijon Kizzee in the Westmont area. Those demonstrations led to more than three dozen arrests, with the protesters accusing deputies of using excessive force and Villanueva saying demonstrators triggered the violence by hurling objects at sheriff's deputies.
Also in the aftermath of the shooting, Villanueva and the sheriff's department are taking criticism over the arrest of a KPCC/LAist reporter while deputies were working to quell the protest outside the hospital. Video from the scene showed deputies pinning reporter Jose Huang to the ground and arresting her.
The sheriff's department claimed she didn't have proper media credentials and was "interfering with a lawful arrest.'' Villanueva later doubled down on that contention, saying Huang got right up on the shoulder'' of a deputy trying to make an arrest, and saying her actions were more "activism'' than journalism.
RELATED: KPCC, LAist reporter's account, video of violent arrest while covering protest seemingly contradicts LA County Sheriff's Department's claims
Video from Huang's cell phone has since surfaced, appearing to contradict the department's description of events. KPCC reported that the video shows Huang repeatedly identifying herself as a reporter, shouting "KPCC,'' and saying, You're hurting me'' while crying out in apparent pain.
City News Service contributed to this report.