Stockholm, Sweden (CNN) -- Authorities on Monday said an unknown gunman thought to be responsible for two shooting incidents in a southern Swedish city may be behind as many as 19 shootings targeting immigrants.
"We started looking from October last year, but it is also very possible that the perpetrator has been active even before that," lead investigator Borje Sjoholm said at a news conference covered by Swedish CNN affiliate TV4.
Police are also investigating DNA found at one of the shootings this weekend, "but we won't know the result of that for still some time," police spokeswoman Sofie Osterheim told CNN.
Cell-phone traffic at the time of the shootings will also be examined for any additional clues, TV4 reported.
A local councilor representing the Sweden Democrats, the far-right anti-immigration party that recently was elected into the Swedish parliament, announced Monday that the party has issued a reward for whomever can give police information about the shooter's identity. The reward is of 25,000 Swedish kronor, equal to about $3,800.
"No other question is more important to us Sweden Democrats than for ordinary people who behave to be able to feel safe in their homes and on our streets," said Per Ramhorn, local Sweden Democrats politician in a statement printed in Swedish media outlets.
The first shooting occurred late Saturday when someone fired a bullet into a small store in central Malmo, police spokesman Calle Persson said Sunday. The second shooting was reported around midnight after a family alerted police to a window being shot, he said.
Both the shopkeeper and the family are immigrants living in the city. Nobody was injured in the most recent incidents.
On Sunday, police said at least 15 shootings in Malmo over the past year might be linked to one shooter, who is believed to have been using a handgun. Sydsvenskan, a regional newspaper, cited police reports that said at least five shootings can be tied to the same weapon.
The shootings have all been well-planned, under the protection of darkness and at places familiar to the shooter, TV4 reported, citing police.
Several of the shootings in Malmo have occurred in recent weeks, police said. However, the first in the series is believed to be an October 2009 shooting that killed a 20-year-old woman, Hans Nilsson, a Malmo police superintendent, told CNN.
"We haven't seen this kind of violence before, specifically targeting immigrants," he added.
Two immigrant women were wounded Thursday evening by gunfire that went through their apartment window.
"I'm almost afraid of turning on the light in my apartment at night now," Shukrije Berisha, who lives in the same building, told the Swedish daily Svenska Dagbladet.
In similar incidents, two men of an "ethnic minority background" recently were shot while waiting at bus stops, according to police.
One of them "was lucky to be alive after being shot in the torso," Nilsson said.
"The shooter was most likely waiting in the bushes before firing his weapon," he said.
Basi Hassan, one of the bus stop victims, told TV4, "I was standing here at the bus stop when I suddenly heard a shot. I don't know where it came from. Then I saw my own blood and I started feeling dizzy."
The Swedish National Murder Commission and Swedish National Criminal Police have launched a major operation, together with local police, to find the gunman.
A group of psychologists is working to establish a profile of the shooter's behavior before, during and after the shootings.
Police also have increased the number of officers and K-9 units patrolling the city.
In Malmo, where nearly one-third of the residents are immigrants, many now fear for their safety. One 17-year-old girl, identified only as Fatima, told TV4 she doesn't go to school by bicycle or bus but will only travel by car.
"I couldn't sleep last night. I just couldn't stop thinking about it," she said.
The recent slew of shootings also has prompted a cell-phone text message that has circulated among Malmo's youth. According to Nilsson, the Malmo police superintendent, the text states: "A killer is lose in Malmo so stay indoors."
"We are very clear that we are not behind this text message, but we can also understand that people are worried," Nilsson said.