Roman Frackiewicz, 44, allegedly attacked Jadwiga Szczygielska at the flat in Pirniefield Bank, Seafield, Edinburgh on April 17 this year.
Prosecutors claim he did inflict or cause to be inflicted "blunt force injuries" to the 77 year-old's head and body by "means unknown".
Frackiewicz faces a separate charge of assaulting the OAP on various occasions between January 1 2016 and the day of the alleged murder.
He is said to have shouted abusive remarks, grabbed her by the shoulders and pushed her.
Frackiewicz today appeared in the dock for a short hearing at the High Court in Glasgow.
Brian Gilfedder, defending, pled not guilty on his behalf adding he was ready for trial.
No trial was set due to the Covid-19 pandemic and judge Lord Mulholland instead fixed a further hearing for December 14 in Edinburgh.