Importune, v. t. [imp. & p. p. Importuned; p. pr. & vb. n. Importuning.]
Etymology: [From Importune, a.: cf. F. importuner.]
1. To request or solicit, with urgency; to press with frequent, unreasonable, or troublesome application or pertinacity; hence, to tease; to irritate; to worry. Their ministers and residents here have perpetually importuned the court with unreasonable demands. Swift.
2. To import; to signify. [Obs.] "It importunes death." Spenser.
2 other Webster entries under this spelling
Importune, a.
1. Inopportune; unseasonable. [Obs.]
2. Troublesome; vexatious; persistent; urgent; hence, vexatious on account of untimely urgency or perinacious solicitation. [Obs.] And their importune fates all satisfied. Spenser. Of all other affections it [envy] is the most importune and continual. Bacon.
Importune, v. i.
To require; to demand. [Obs.] We shall write to you, As time and our concernings shall importune. Shak.
Shades of meaning
Fernald has no entry of its own for importune; he lists it under pray.
He lists it without comment; the entries above explain its neighbors.