The representatives of Stop & Shop and the union are expected to continue negotiations on Sunday morning after the two parties meet on Saturday.
The company said the two sides had discussed new contracts for 31,000 workers in New England and planned to meet again on Sunday.
Stop & Shop employees left work Thursday across Massachusetts and New England.
Several stores in Massachusetts, Connecticut and Rhode Island reopened on Friday, but there were fewer in some places due to the strike.
In a video on Facebook, Tyrone C. Housey, president of UFCW Local 1459 in Springfield, asked union members to kindly ask customers not to do business with the company during the strike.
Workers at Stop & Shop United Food and Commercial Workers International in Massachusetts, Connecticut and Rhode Island have been without a contract since the end of February.