imply then? That food offered to idols is anything, or that an idol is anything? [20] No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be partners with demons. [21] You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons. (cf. 9:13)

Romans 15:15-17 But on some points I have written to you very boldly by way of reminder, because of the grace given me by God [16] to be a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable, sanctified by the Holy Spirit. [17] In Christ Jesus, then, I have reason to be proud of my work for God.

“Offering”? Offering of what? “Priestly service”? The word for “priestly service” is hierourgeo: Strong’s word #2418. It is defined by Strong (my hardcover copy from Riverside Book and Bible House) as “to be a temple-worker, i.e., officiate as a priest (fig.): — minister.” The online version (linked above) has “to minister in the manner of a priest, minister in priestly service.” It also notes (from Thayer’s Greek-English Lexicon) historical etymological definitions of “to be busied with sacred things; to be perform sacred rites” (from Philo), and “used esp. of persons sacrificing” (from Josephus). Compare Baptist Greek scholar A. T. Robertson for the basic definition: “to work in sacred things, to minister as a priest.”

Marvin Vincent’s Word Studies in the New Testament states (for Rom 15:16):

Ministering (ierourgounta). Only here in the New Testament. Lit., ministering as a priest.

Offering up (prosfora). Lit., the bringing to, i.e., to the altar. Compare doeth service, John xvi. 2.

Gerhard Kittel’s Theological Dictionary of the New Testament (abridged one-volume edition, p. 354) defines it as “‘to perform sacred or sacrificial ministry.’ In Josephus and Philo it always means “to offer sacrifice” and often has no object. (hierourgia means “sacrifice” and hierourgema the “act of sacrifice.”)”

A Catholic Commentary on Holy Scripture (London: Thomas Nelson & Sons Ltd., 1953, Dom Bernard Orchard, General Editor), provides further helpful analysis:

The essential point in every explanation is to realize that the sacrificial terms used here are metaphorical, and that therefore this verse cannot be quoted against the existence of a specially consecrated priesthood in the Church when Paul wrote . . . The difficulties lie in the analysis of the metaphors. . . . To bring the Gentile world as a worthy sacrifice to the altar of God is probably all that Paul meant to say. For the same idea cf. Is. 66:19 f.

The Eerdmans Bible Commentary (Protestant, p. 1044) concurs:

Paul describes his divine commission in terms of the priesthood: a minister (Gk. leitourgos; lit. a ‘priest’; cf. Heb. 8:2), in the priestly service (Gk. hierourgon) and offering (Gk. prosphora) are three sacerdotal terms.

Thus, Paul has called himself a priest — using two different terms. We get the word liturgy from litourgos (Strong’s word #3011; cf. 3008, 3009, and 3010). Strong’s online, for word #3008 (litourgeo) applies it to, among other things, “priests and Levites who were busied with the sacred rites in the tabernacle or the temple.” The author of Hebrews applies one of these terms to priests in the Old Covenant sense in Hebrews 9:21; 10:11 and to Jesus as high priest in 8:2.

Given the central motif in the New Testament of Jesus as the sacrificial lamb, it stands to reason that the Sacrifice of the Mass would be associated with the Eucharist, as the central rite of Christian worship.