When Christ instituted the New Covenant, He abolished Old Testament sacrificial, dietary, and ceremonial laws. The only ceremony clearly commanded in the New Testament is communion (1 Corinthians 11:23-26).
Most denominations hold one of two views:
1. All of the 10 Commandments, including the Fourth, are permanent laws.
2. The Fourth Commandment is no longer a law but the principle of having a weekly time of rest and reflection is a godly principle.
The early New Testament Church was serious about fellowship and worship, and we're commanded to have fellowship with other Christians (Hebrews 10:24-25), but no particular day or days are specified in the New Testament.
When we're saved, we experience the ultimate and final rest--a rest from our works and dependence on the Grace of Christ. In Christ, every day becomes a spiritual Sabbath (Hebrews 4:4-11).
Whatever we believe about the Sabbath, we are commanded to respect our differences (Romans 14). It's an area where Christians will apply Biblical principles in differing ways.
Colossians 2:16-17 is a fitting conclusion to this post:
"So don’t let anyone condemn you for what you eat or drink, or for not celebrating certain holy days or new moon ceremonies or Sabbaths. For these rules are only shadows of the reality yet to come. And Christ himself is that reality."
(1) Note: This doesn't mean the word "Sabbath" is not found in the N.T. The word and the practices are mentioned on several occasions, most notably when Jesus is doing something that violates Jewish Sabbath laws. But there are no N.T. commands regarding the Sabbath.
See also Galatians 4:10-11 where Paul fears that the Galatians had exchanged the grace of Christ for the old system of law-keeping and writes: "You are trying to earn favor with God by observing certain days or months or seasons or years. I fear for you..." (Galatians 4:10-11, NLT)
copyright, Gail Burton Purath, 2013, BiteSizeBibleStudy.blogspot.com
Another article on this subject: Sabbath Keeping and the New Covenant