refuse verb

She refused to gowith her friend. 

She refused toanswer the question 

He refuse to leave

They offered me ajob that I couldn't refuse. (I couldn't refuse the job)

I politely refusedtheir invitation.

I politely turn down their invitation

Why didshe turn down your invitation?

Why didshe refuse to accept your invitation?

The carrefused to start.

The big clock refused to welcome the New Year

 reject verb

The manager rejectedhis plan. The manager refused to accept his plan

He rejected the application. The application was rejected.  

rejection

the rejection letter

refuse noun  /ˈrefjuːs/

refusal noun

 the refusal of a request/an invitation/an offer