In your question you ask about a Universal Church. First off, There is no "Universal Church" mentioned in the Bible, at least not the NKJV. However, the idea that there is one Church for all mankind is found in the Bible. Eph 4:4-5 says

"There is one body, and one spirit, even as you are called in one hope of your calling, one lord, one faith, one baptism..." (Ephesians 4:4-5)

Also in Matthew 16:17-18, Peter had just confessed that he believed that Jesus was the son of God. Verse 18 says "...and upon this rock I will build my Church." (Not on peter but the truth that Jesus Christ is the son of God). Notice that he didn't say "Churches".

Finally we read in John 17:20-21 about how the lord was praying for unity for those who believed and for those who would believe. He prays that they might be one.

In order to be one united we would all have to teach the same thing. "Now I beseech you brethren by the name of our lord Jesus Christ, that ye all speak the same thing (one lord one faith one baptism etc...) and there be no divisions among you; But that you be perfectly joined together in the same mind and in the same judgment." (1 Corinthians 1:10)