In the letter Ian Blackford also continues his calls for Dominic Cummings to resign.
The PM has been urged to announce a 'financial package for people' to support them through the coronavirus outbreak.
Some MPs cheered as royal assent was confirmed for the European Union (Withdrawal Agreement) Act.
The European Union (Withdrawal Agreement) Bill was passed by 330 votes to 231.
Boris Johnson told MPs during Prime Minister's Questions that the people of Scotland "voted decisively" in 2014 to stay in the UK in a "once in a generation choice".
The Ross, Skye and Lochaber MP has been unanimously re-appointed at the parliamentary party's AGM.
The SNP Westminster leader said the general election 'reaffirmed the mandate' for a referendum.