Error arises on clicking the .exe file. The dialog box says "An unexpected error while unpacking files. Error code: -2147467259". File name is "ArcGISPro_26_175036.exe"
It may be a bad download. Did you try to download it again? (Download to a simple, short folder path, eg c:/Temp)
I tried keeping the file at simple locations like D:/ArcGIS or C:/ArcGIS and extracting to similar simple locations as you suggested. But the error persists. I have used the same file earlier to install it and it was running good.
Do I need to install something else on my system since I did a fresh install of windows after which I am attempting to install ArcGISPro2.6.
I assume that you are trying to reinstall arcgis pro and have uninstalled previous installations.
If so, and you have already run the *.exe file successfully once, then locate the *.msi in the extracted folder and run it.
The *.exe extracts a *.msi and *.cab file into a sub folder in your download folder.
Anything other than a valid first time install by running the *.exe will most likely cause failure.