I heard that in Hinduism, we must beget offspring after marriage as part of Hindu belief (Pitru Runa). In other words is there scripture about the importance of carrying on a blood line? Is it mandatory to follow it? If so, what scriptures describe this?
Yes, if you marry you need to grow your lineage. According to Shatapath Brahmana, there are four types of debt to everyone as: debt to Gods (Deva Rina), debt to Rishis (Rishi Rina), debt to Fathers (Pitri/Pitru Rina) and debt to Men (Manava/Manushya Rina).
To get free from Pitri Rina you should grow your lineage.
And further, inasmuch as he is bound to wish for offspring, for that reason he is born as (owing) a debt to the fathers: hence when there is (provided by him) a continued, uninterrupted lineage, it is for them that he does this.
Similar thing has been said in Yajurveda, Taittiriya sanhita.
A Brahman on birth is born with a threefold debt, of pupilship to the Rsis, of sacrifice to the gods, of offspring to the Pitrs. He is freed from his debt who has a son, is a sacrificer, and who has lived as a pupil