Enteuxis (ἔντευξις, G1783) means intercession, petition, prayer — especially prayer on behalf of others or direct approach to a superior. From entynchano (to approach, to meet with, to petition). It appears in 1 Timothy 2:1 — 'I urge, then, first of all, that petitions, prayers, intercession (enteuxeis) and thanksgiving be made for all people' — and 1 Timothy 4:5 — 'because it is consecrated by the word of God and prayer (enteuxeōs).'
Enteuxis carries the rich sense of approaching a king with a petition — an audience with the sovereign on behalf of another. In 1 Timothy 2:1, Paul places it within a taxonomy of prayer: petitions, prayers, intercessions, thanksgivings — enteuxis being the intercessory element, reaching out toward others. The theological foundation is the intercession of Christ Himself: Romans 8:34 — 'Christ Jesus who died — more than that, who was raised to life — is at the right hand of God and is also interceding for us.' Hebrews 7:25 — 'he always lives to intercede for them.' Our prayers of enteuxis participate in the intercessory work of Christ. When we pray for 'all people' (1 Timothy 2:1), we extend the reach of Christ's intercession through His body on earth. Intercession is the most Christlike form of prayer — it displaces self-concern and stands in the gap for another.