"We have followed all the rules, regulations and laws of the land," Mr Asif told lawmakers.
India has called the sentencing of Mr Jadhav - a retired Navy official arrested last year and accused by Pakistan of spying - "pre-meditated murder" and said it will do "whatever it takes" to save him. Describing the proceedings that led to the 46-year-old's conviction as "farcical", the government has also alleged that it had requested consular access 13 times had been denied it.
Mr Asif said Pakistan "will not grant any concessions to elements working against the security and stability of the country, whether they're operating from inside Pakistan or from outside it".
Earlier, Pakistan Prime Minister Nawaz Sharif said his country wants good relations with all countries, "particularly its neighbours", but said its armed forces are fully capable and prepared to respond to "any spectrum of threats".
Calling Pakistan a "peace-loving nation", Mr Sharif asserted that "despite our desire for peaceful coexistence, we cannot remain oblivious to defending our sovereignty and protecting our independence."
Relations between Pakistan and India have been frosty since last year's attack by Pakistani terrorists on an army camp in Kashmir's Uri, in which 19 military personnel were killed.
As parliament jointly condemned Kulbhushan Jadhav's death sentence, Foreign Minister Sushma Swaraj warned that Pakistan should "consider the consequences" for ties if the retired navy man was hanged.
Rubbishing Pakistan's charges against Mr Jadhav, the government said he was kidnapped in Iran and "his subsequent presence in Pakistan has never been explained credibly".
With inputs from PTI