Prevarificate / Equivocate

Prevaricate means
>The fact of avoiding telling the truth or saying exactly what you think.
>Speak or act in an evasive way.

Lie is the blunt term, imputing (Means – Representing) dishonesty. lied about where he had been prevaricate softens the bluntness of lie by implying quibbling (means – the action of raising objections about a trivial matter) or confusing the issue.

Equivocate which means use ambiguous language so as to conceal the truth or avoid committing oneself is often used as a synonym for prevaricate.

Example

All my attempts to question the authorities on the subject were met by prevarication
It was his prevarication that caused him to lose the election.
The altered plans and prevarication made everyone nervous.
The government have equivocated too often in the past
Officer continued to equivocate when the CBI persisted in their questioning