UK Government says the cash takes the amount allocated through the Barnett formula since pandemic began to £9.7bn.
The Scottish Government says taxing the new £500 payment could mean fewer people apply.
Scottish Government analysis found extending the scheme until next June would bring major economic benefits.
Chancellor visits Glasgow and the Isle of Bute amid row over Scotland's borrowing powers.
Chancellor Rishi Sunak will deliver his first UK Budget later amid calls for additional support and measures to tackle Covid-19.