"Our Embassy in Kabul was again subjected to yet another terrorist attack, which has resulted in injury of Indian security personnel as well as death of large number of Afghan civilians," Puri told the committee of the General Assembly that handles a range of social, humanitarian affairs and human rights issues.
"While it is important for the international community to condemn terrorism and these attacks in an unequivocal manner, it is also critical that we strengthen the legal framework in the fight against terrorism," he noted.
Earlier, UN Chief Ban Ki-moon condemned the attacks at the Indian embassy. The Security Council also deplored the "reprehensible" attack demanding that those responsible be brought to justice.
On its website, the Taliban write that one of their "martyrs" carried out suicide car bomb attack in a heavily fortified diplomatic area and added that the Indian embassy "was the main target".
The top Indian diplomat stressed that in view of the growing threat of terror attacks, it was time to wrap up the draft for the the 'Comprehensive Convention on International Terrorism (CCIT)' since the document had been under negotiations for years.
"Countless innocent lives have been lost to heinous terrorist attacks. It is imperative that our resolve against perpetrators of such attacks now be manifested in a strong and resolute manner," Puri said.
"It is time for the global community to conclude the negotiations and make a firm commitment by adopting the Convention," he added.
A revised draft of the treaty was submitted by India in 2001 to the UN. It is now stuck for a variety of legal and technical issues including differences over the definition of terrorism.