Asseverate, v. t. [imp. & p. p. Asseverated; p. pr. & vb. n. Asseverating.]
Etymology: [L. asseveratus, p. p. of asseverare to assert seriously or earnestly; ad + severus. See Severe.]
To affirm or aver positively, or with solemnity.
Syn. -- To affirm; aver; protest; declare. See Affirm.
Shades of meaning
Fernald has no entry of its own for asseverate; he lists it under allege, state.
Where he writes about it:
It has more solemnity than declare, and more composure and dignity than asseverate, which is to assert excitedly. — from state