I urge, then, first of all, that requests, prayers, intercession and thanksgiving be made for everyone—for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness. This is good, and pleases God our Savior, who wants all men to be saved and to come to a knowledge of the truth. For there is one God and one mediator between God and men, the man Christ Jesus, who gave himself as a ransom for all men-- the testimony given in its proper time. And for this purpose I was appointed a herald and an apostle-- I am telling the truth, I am not lying--and a teacher of the true faith to the Gentiles.
Essentially, the prayers recommended here are prayers for the progress of the gospel. One means to that end is prayer for the wisdom and well-being of the imperial and regional political leaders in maintaining peace and order in the empire. Christian apologists of the early centuries were able to point to these practices to show that they were not anti-Roman, even if they did not worship the emperor as most residents of the empire did. These prayers may have been in direct contradiction to the false teaching at Ephesus.
Here Paul gives Timothy and the Ephesians three reasons to pray for the universal progress of godliness. First, in the sense that God desires obedience for all of his commands, God desires that everyone come to acknowledge the apostolic testimony, that is, “the truth” (v. 4). So praying for the conversion of everyone is consistent with God’s moral demand on everyone to heed the gospel. Second, for all humankind, there is only one God. Because conversion entails repentance from false idols (1 Thess 1:9) and dead works (Heb 6:1), it pleases God to pray for the conversion of those who worship that which is not God. Third, for all humankind, there is only one Savior. “Salvation is found in no one else, for there is no other name under heaven given to men by which we must be saved” (Acts 4:12). Because conversion entails despising all false hopes and turning to Jesus, it pleases God to pray for the conversion of those who hope in that which is not Christ.