The Collaborative International Dictionary of English v.0.48:
Importune \Im`por*tune"\, v. t. [imp. & p. p. Importuned
([i^]m`p[o^]r*t[=u]nd"); p. pr. & vb. n. Importuning.]
[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.
[1913 Webster]
Their ministers and residents here have perpetually
importuned the court with unreasonable demands.
--Swift.
[1913 Webster]
2. To import; to signify. [Obs.] "It importunes death."
--Spenser.
[1913 Webster]