In a statement, Singh said the government is determined to foil the designs of those who want to disrupt peace through such a terror attack "sponsored and sheltered by Pakistan".
"Jaish-e-Mohammed has carried out this terror attack. We assure the country that we will undertake whatever it takes to avenge this," he said.
His deputy Kiren Rijiju said the "cowardly" attack will not go unpunished and it will be avenged in "all way possible".
The convoy had started from Jammu around 3.30 am and was supposed to reach Srinagar before sunset, officials said.
The number of personnel travelling back to the Valley was high as there was no movement on the highway for the last two to three days because of bad weather and other administrative reasons, they said.
Usually, about 1,000 personnel are part of a convoy but this time it was a total of 2,547 personnel.
A road opening party was deployed and the convoy had armoured counter-terror vehicles, officials said.
As news of the magnitude of the attack came in, political leaders from across the spectrum spoke out in condemnation and to condole the deaths of the security personnel.
Former Jammu and Kashmir chief ministers Omar Abdullah and Mehbooba Mufti also condemned the attack in the strongest terms.
Rajnath Singh, who also spoke to Governor Satya Pal Malik and took stock of the situation, cancelled his engagements in Bihar on Friday. Union Home Secretary Rajiv Gauba cut short his visit to Bhutan.
A team of National Investigation Agency and National Security Guards will leave for Kashmir Friday morning to assist in the investigation.
This was the first suicide car bomb attack in Kashmir since the 2001 strike on the Legislative Assembly in which 41 people, including three suicide attackers, were killed.
The scene of Thursday's attack is not very far from the Commando Training Centre at Lethpora, which was stormed by Jaish militants on December 31, 2017, killing five CRPF personnel.
The Srinagar-Jammu national highway has been a favoured route for militants to target security forces.
The CRPF bore the brunt of a militant attack at Pampore, less than seven km from Lethpora, in June 2016, losing eight jawans while 22 others sustained injuries.
In an attack on the Uri military base in September 2016, Jaish militants killed 18 Army jawans and injured dozens of others. The ferocity of the attack led to India conducting a surgical strike against Pakistan.