BRUSSELS, March 20—The capture of accused Paris attacker Salah Abdeslam yielded crucial insight into how he used local connections to hide in the Belgian capital for months and led to his admission he was preparing to strike again, officials said.

Friday’s arrest of Mr. Abdeslam several hundred yards from his family home has left authorities trying to determine the extent to which Europe’s most wanted man relied on friends and family to stay undetected since the Nov. 13 attacks. They said the investigation into the Paris attacks so far suggests that fighters trained in Syria could tap such a network of local sympathizers to prepare new strikes.

“We have found a lot of weapons, heavy weapons, in the first investigations and we have found a new network around him in Brussels,” Belgian Foreign Minister Didier Reynders said Sunday. He added that the French-Belgian investigation had discovered more than 30 people involved in the Paris attacks.

“But we are sure there are others,” he said.

European authorities say they are searching for at least one Syrian-trained fighter who worked with Mr. Abdeslam. And Belgian officials said the network is much larger than they previously suspected. In Brussels on Sunday, a heavy police and army presence guarded train stations and the city’s main tourist areas.

The combination of experienced jihadists with no prior connection to Belgium and individuals with local knowledge is a key focus of

investigators anxious to prevent further attacks and break open the Islamic State terror network.

Mr. Abdeslam was assisted before and after the Paris attacks by a group of at least three trained fighters with ties to Islamic State, officials said. One of the men is dead, and a second has been captured. A third—known by the alias Soufiane Kayal—remains at large, Belgian authorities said.

According to Paris prosecutors, Mr. Abdeslam told Belgian investigators that he had intended to blow himself up on Nov. 13 with other suicide bombers at the Stade de France soccer stadium. But he said he changed his plans at the last moment. Mr. Abdeslam’s lawyer said Sunday that his client was cooperating with authorities, though he planned legal action against the French prosecutor for allegedly revealing details of confidential Belgian court proceedings. Mr.

Reynders, the foreign minister, said Mr. Abdeslam told prosecutors he had been ready to carry out follow-up attacks.

Another radical fighter—an Algerian man whom police identified as Mohamed Belkaid—was shot dead last Tuesday while holding police at bay by firing a Kalashnikov from an apartment window. Mr. Abdeslam and a man believed to be a Syrian-trained fighter using the alias Amine Choukry had been hiding inside and were able to escape, authorities say.

“People are coming over from Syria constantly,” said Belgian Justice Minister Koen Geens on television on Sunday. “They are unknown to us; often they haven’t been to Europe before. That’s a challenge we face: the cooperation between local networks that are very integrated and people who are trained and come from the Middle East.”

Belgian investigators said they were struck at the fanaticism and violence they encountered in the Tuesday raid. When Mr. Belkaid opened fire with an assault rifle, he “knew he was not going to come out alive,” said one Belgian official. “This shows the level of training and determination these people have,” the official said.

Belgian officials say two months before the November Paris attacks, Mr. Abdeslam linked up with the fighters from Syria. Mr. Abdeslam picked up both Mr. Kayal and Mr. Belkaid in Budapest, where they had taken cover in the wave of Syrians fleeing war, officials said. A U.S. official said Islamic State has been hiding fighters without European passports in the flow of migrants. “They are taking advantage of the migrant crisis,” said the official.

Investigators haven’t determined precisely where Mr. Abdeslam met the other fighter, Mr. Choukry, and brought him to Brussels, but it was also allegedly ahead of the Paris attacks. The two men were stopped and fingerprinted in Germany on Oct. 3.

But it was a network of childhood friends, family members and fellow petty criminals that apparently helped Mr. Abdeslam and the Syrian-trained fighters stay under cover immediately before and after the Paris attacks, authorities said. Without their assistance, they said, he couldn’t have remained at large for four months.

A French national, the 26-year-old Mr. Abdeslam grew up in Molenbeek, a poor but gentrifying neighborhood of Brussels with a large Muslim population. Molenbeek appears to be one of the places where the Paris attackers organized the November terror assault and has long been the focus of counterterror investigations by Belgian authorities.

On the night of the Nov. 13 attacks, Mr. Abdeslam is suspected of escaping from Paris with the help of childhood friends from Molenbeek—Hamza Attou and Mohammed Amri—who drove him back to Brussels. The pair admit driving him back but say they had nothing to do with the attacks and didn’t know of his involvement.

Another Brussels friend, Ali Oulkadi, admitted to having driven Mr. Abdeslam on the day after the attacks to another Brussels district, where police later found one of Mr. Abdeslam’s hide-outs, according to his lawyer. Mr. Oulkadi said he hadn’t previously known of Mr. Abdeslam’s involvement.

Officials say Mr. Abdeslam didn’t go into hiding in Molenbeek for the entire four months. Instead, he moved around Brussels, squatting in houses that weren’t in use or abandoned—such as the apartment in

houses that weren’t in use or abandoned—such as the apartment in the Brussels neighborhood where a the gunbattle broke out on Tuesday, just a few days before his capture.

Another apartment where Mr. Abdeslam is believed to have returned to after the Nov. 13 attacks is in the neighborhood of Schaerbeek, where police said they found evidence that the suicide vests used in Paris had been assembled.

Under the Radar

From the time suspect Salah Abdeslam fled Paris after the Nov. 13 attacks, Belgian authorities believe he was hiding out in several Brussels neighborhoods. He was arrested in his home district, some 500 yards from his grandmother’s house.

Molenbeek district counselor Ahmed El Khannouss, who knew Salah Abdeslam and his family, said the fugitive couldn’t have hidden for so long if he had relied only on his childhood friends and family members.

“It’s not correct to say he was in Molenbeek all the time. He was taken to places that are cut off from society—the flat in (the Brussels district) Forest had no electricity or water. Only in the end, he spent three to four days in the basement of his cousin,” Mr. El Khannouss said.

The gunbattle on Tuesday provided investigators with the hard evidence they needed that Mr. Abdeslam was still in Brussels. The funeral this past Thursday of Mr. Abdeslam’s brother, one of the suicide attackers in Paris, also provided the investigative break that they needed to catch him.

One of the men at the funeral, Abid Aberkan, is a distant cousin of Mr. Abdeslam. According to investigators, Mr. Aberkan had offered his mother’s house to shelter Mr. Abdeslam in Molenbeek after the gunbattle. According to local officials, police began monitoring many of the people attending the funeral.

From the surveillance they learned of a mobile number possibly being used by Mr. Abdeslam. That number led police to the Molenbeek apartment where Mr. Abdeslam was hiding, the officials said.

Mr. Aberkan remains in custody after being charged with participation in the activities of a terrorist organization and for hiding criminals. Nathalie Gallant, who represents both the families of Mr. Abdeslam and of Mr. Aberkan, told Belgian television that the two families were linked but said Mr. Aberkan had nothing to do with the attacks.

—Natalia Drozdiak and Matthias Verbergt contributed to this article.

Corrections & Amplifications:
Nathalie Gallant represents the families of Salah Abdeslam and Abid Aberkan, a distant cousin of Mr. Abdeslam. An earlier version of this article misspelled Ms. Gallant’s last name. (March 20, 2016)