hasten
/ˈhā-sᵊn/
verb
to move or act quickly
to encourage to move or act quickly : to urge on
to cause to happen more quickly : accelerate
She hastened up the stairs.
idiom
to immediately say something in order to prevent confusion or misunderstanding
The company announced that the initial tests look promising, but they hastened to add that there is still much more testing to be done.