As a leader, you cannot orient every Sunday morning service around unbelievers. The believers would then be left untaught and immature, knowing only the basic truths of salvation. Through the careful teaching and explanation of God’s word, a Sunday morning service should equip believers and strengthen them spiritually to do the work of the ministry (Ephesians 4:12-14).
If you do then direct a Sunday morning message to believers, how do you reach out to the lost without losing the emphasis the message has to believers? Possible ways are through a testimony, the introduction of a congregational hymn that speaks to unbelievers, or special music designed with unbelievers in mind.
As a pastor, you can also reach out to the lost at the conclusion of the message after a closing prayer yet before the final song. Consider the following segue:
My message has been directed to those who know beyond any doubt that if they were to die, they would go to heaven. It has been directed to believers. But maybe you are here and you don’t know for sure you would go to heaven. The Bible makes the plan of salvation so simple: all of us have to come to God recognizing that we are sinners who deserve to be separated from Him forever. But 2000 years ago, Jesus Christ paid the price for our sins by dying on a cross in our place. He was our substitute. They punished him where they should have punished us. The third day he arose, proving that God accepted His Son’s death in our place. So if you simply put your trust in Christ alone, not Christ and your church attendance, or Christ and your good life, but Christ alone as your only way to heaven, God will give you eternal life as a completely free gift. If you have not trusted Christ as your Savior, I would love to talk with you.
You can tell them how to settle their salvation right there in their seat and then come forward. You could also invite them to meet you after the service or even to call you that week.
An invitation handled in the above way does not lighten the thrust of your message to believers but does reach out to the unbeliever.