Jesus kept the old Jewish law Sabbath because He came to fulfill the Law, not abolish it. However, He did not observe the old Sabbath in the same manner as the Jews. Instead, He proved He was Lord of the Sabbath (Matthew 12:8; Mark 2:27-28; Luke 6:1-9). Jesus saw that the Sabbath was made for man, as a holy day of rest. But men were trying so hard to keep it that they had no rest at all! He knew that if men continued to be as strictly bound to the Sabbath, then the bondage of the Old Covenant would be brought into the new one.
The Church is not living under the Law. We are living under grace. Romans 7:6 says, "Now we are delivered from the law, that being dead wherein we were held; that we should serve in newness of spirit, and not in the oldness of the letter [law]." Galatians 3:10-14 is another good example of this truth. We have been set free.
Nevertheless, even in its early days, Paul had to warn the Church to not fall back into bondage regarding the Sabbath. "Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days: Which are a shadow of things to come; but the body is of Christ" (Colossians 2:16-17).
The New Testament does not demand man to keep any particular Sabbath (Romans 14:5-6; Galatians 4:9-10; Colossians 2:14-17). We know, however, that observance of the Sabbath day continued even after the Church's beginning because the Jews met in the synagogue on the Sabbath. Paul preached to the Jews on that day. Nonetheless, not one time is it recorded that Christians gathered on the old Jewish Sabbath. They gathered on the first day of the week - as most Christians do today.
This custom began because Jesus was raised from the dead on the first day of the week (Mark 16:9). Today, we understand what is important is that we follow God's example and have one day a week set aside as a holy time of rest and fellowship.
So, even though we are no longer under law to keep the Sabbath, the Bible says believers should not forsake gathering together and encouraging one another. It's our job to motivate each other to love and good works (Hebrews 10:24-25).
Love fulfills the royal law. The only commandment the Church has is to walk in love. "This is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment" (1 John 3:23). This is the fulfilling of the Law.