It was unclear how many militants were involved in the attack.
All three were based in Pulwama in south Kashmir for the a year ago, the officials said, citing intelligence reports and JeM's claims on various social media platforms, including Facebook and Whatsapp.
Anti-Indian sentiment runs deep among Kashmir's mostly Muslim population.
In a separate incident, officials from India's paramilitary Central Reserve Police Force (CRPF) said they had routed a small group of militants who the day before tried to storm one of their bases in Kashmir's main city of Srinagar.More news: Icardi to Man United is Mino Raiola's intention
More than 70,000 people have reportedly been killed in the conflict since 1989.
India accuses Pakistan of arming and training the militants, a charge it denies.
Hours after defence minister Nirmala Sitharaman vowed to hit Pakistan for the Jammu terror attack, her Pakistani counterpart Khurram Dastgir Khan warned that his country will "pay India in its own coin in case of any Indian misadventure".
The Defence Minister said, evidence against the terrorists has been compiled and will be given to Pakistan.More news: Physicians Realty Trust (NYSE:DOC) Stock Is Shorted More
Saturday's attack on the camp near Jammu, the winter capital of the state, was the worst in months with six soldiers and the father of a soldier killed.
Ms Sitharaman added that an alert had been sounded on the likelihood of terrorist attack around this period and accordingly, Quick Reaction Teams were positioned in vulnerable areas. Three terrorists were also killed in the operation.
The body of the army soldier was recovered during the clearance operation at the camp last night, said Jammu-based army public relation officer Lt Col Devender Anand.
Sitharaman said the three militants were all Pakistanis and were handled by their Jaish-e-Muhammad leaders across the border. This happened two days after suspected Jaish-e-Mohammed militants attacked the Sunjuwan Army camp in Jammu. According to reports, two motorcycle borne youth came close to the periphery boundary wall of army camp in Domana. She also spoke about locals aiding the terrorists. "We will not let anybody down", she said, when she was told that the FIR was registered against the troops only after the Chief Minister had spoken to her. "Intelligence inputs indicate that these terrorists were being controlled by their handlers from across the border", the minister said late on Monday. Evidence are being scrutinised by NIA.More news: Vladimir Putin meets Federation Internationale de Football Association president Gianni Infantino to discuss World Cup
He said the Centre takes a call on talks with Pakistan and there was no scope of interference by others. It will have to be proved over and over again that they are responsible. "Soldiers' sacrifice won't go in vain; we would ensure that Pakistan pays the price for its misadventure at a time of our choice", she said. "Both sides, accordingly, agreed to a Comprehensive Bilateral Dialogue and directed the foreign secretaries to work out modalities and schedule of the meetings under the dialogue including peace and security, CBMs, Jammu & Kashmir, Siachen, Sir Creek, Wullar Barrage/Tulbul Navigation Project, economic and commercial Cooperation, counterterrorism, narcotics control and humanitarian issues, people to people exchanges and religious tourism", the statement had stated.