The hortative mood and the exhortative mood are largely synonymous with this, although sometimes distinctions are made. When distinctions are made, together they are called "hortative moods". See Johan van der Auwera, Nina Dobrushina, Valentin Goussev, "A Semantic Map for Imperative-Hortatives", in Dominique Willems, Timothy Colleman & Bart Defrancq (eds.) Points of Comparison in Linguistics: from Morphology to Discourse. Basingstoke: Palgrave Macmillan for some discussion of when these distinctions are made.
In defending misconduct allegations as administrator of the General Services Administration at a 13 June 2007 hearing of the United States House Committee on Oversight and Government Reform, Lurita Doan stated that she "thought she was using like a hortatory subjunctive right there" when she told the United States Office of Special Counsel earlier under oath, "Until extensive rehabilitation of their performance occurs, they will not be getting promoted, they will not be getting bonuses or special awards or anything of that nature." U.S. Rep. John Sarbanes disagreed saying this was "clearly the [common] future tense" adding that the "best example of the use of hortatory subjunctive" is when she allegedly said (in violation of the rule of law, specifically the Hatch Act), "How can we help our candidates?" at a 26 January 2007 GSA meeting, which he defined as "an exhortation in the subjunctive tense [sic] not using the word 'let's' as is usually seen, but using this other construction.
While not found in modern Hebrew, the cohortative mood has an important role in Biblical Hebrew, where it was represented by a lengthened future form; namely adding the vowel 'ā' (adding of the letter ה) at the end of an already conjugated verb.
|"And God said, Let us make man in our image, after our likeness..."|
|"ויאמר אלהים נעשה אדם בצלמנו כדמותינו..."|
The verb "let us make" (נעשה) is problematic -- it is found in an apparent plural form, but Judaism is a monotheistic religion. Some authors explain this as a true plural -- God consulting the angels, in Jewish tradition; the Trinity speaking among themselves, in Christian -- but it's likelier to have come from the now-extinct cohortative mood.