The militants, suspected members of Hizb-ul-Mujahedin, also wounded 13 soldiers in the three attacks, The Times of India reported.
Defense sources told The Times of India a carload of terrorists and two on a motorcycle fired automatic weapons at a convoy of 35 Rashtriya Rifles soldiers around 4:30 p.m.
The terrorists fled the scene and then attacked a police post at a bridge before attacking another police checkpoint and exchanging fire with security forces.
Hizb-ul-Mujahedin claimed responsibility for the attack and warned more ambushes were imminent, The Times of India reported.
The attacks come after an another ambush in Srinagar when militants killed two police constables in a daylight ambush in the center of the city on Saturday.
Hizb-ul-Mujahedin -- meaning Party of Holy Warriors -- was formed in 1989 and is designated a terrorist organization by India and the European Union.
The group, whose current leader is a Kashmiri known under the alias of Sayeed Salahudeen, is fighting for the integration of India's Jammu and Kashmir state with neighboring Pakistan, security analyst GlobalSecurity.org reported.
Pakistan claims all the Kashmir region of India's Jammu and Kashmir, which is around 60 percent Muslim -- India's only Muslim majority state.
Pakistan and India have fought several wars over the territory but agreed on a cease-fire line in 2003.
Hizb-ul-Mujahedin was formed reportedly as the militant wing of Jamaat-e-Islami at the behest of the Pakistan's state security intelligence organization Inter Services Intelligence, GlobalSecurity.org said.
ISI was looking for another Kashmiri militant group to counter the Jammu and Kashmir Liberation Front, which advocated complete independence of the Jammu and Kashmir and not succession to Pakistan.
Many of the early Hizb-ul-Mujahedin members were former JKLF members, GlobalSecurity.org reported.
Hizb-ul-Mujahedin remains closely linked to Jamaat-e-Islami in the upper Kashmir Valley and in Pakistan. Overseas, it allegedly is backed by Ghulam Nabi Fai's Kashmir American Council and Ayub Thakur's World Kashmir Freedom Movement in the United States.
The specialist anti-terror force Rashtriya Rifles is a favored target of many militant groups.
Earlier this month, a 19-hour gun battle between rebels and a foot patrol of 44 Rashtriya Rifles soldiers in Kashmir left two militants dead.
The attack was carried out by suspected members of Jaish-e-Mohammad -- Army of Mohammad -- based in Pakistan that was responsible for the 2001 attack on the Indian Parliament that left nine people dead and put the organization on the radar of security forces around the world, The Times of India reported in February.
During his two-day visit to Kashmir, Prime Minister Singh is expected to officially open two hydro-power projects.