The Collaborative International Dictionary of English v.0.48:

Asseverate \As*sev"er*ate\, v. t. [imp. & p. p. Asseverated;
   p. pr. & vb. n. Asseverating.] [L. asseveratus, p. p. of
   asseverare to assert seriously or earnestly; ad + severus.
   See Severe.]
   To affirm or aver positively, or with solemnity.
   [1913 Webster]

   Syn: To affirm; aver; protest; declare. See Affirm.
        [1913 Webster]

WordNet (r) 3.0 (2006):

asseverate
    v 1: state categorically [syn: assert, asseverate,
         maintain]

Moby Thesaurus II by Grady Ward, 1.0:

57 Moby Thesaurus words for "asseverate":
   acknowledge, affirm, allege, announce, annunciate, argue, assert,
   assever, attest, aver, avouch, avow, bear witness, certify,
   confess, contend, declare, depone, depose, disclose, enunciate,
   express, express the belief, give evidence, have, hold, insist,
   issue a manifesto, lay down, maintain, manifesto, nuncupate,
   predicate, proclaim, profess, pronounce, protest, put, put it,
   quote, recite, relate, say, set down, speak, speak out, speak up,
   stand for, stand on, state, submit, swear, testify, vouch, vow,
   warrant, witness