For Letters of Regret
I write at once to thank you, regretting most sincerely that——
I very much regret that I cannot accept your kind invitation to——
I regret that a previous engagement will prevent my acceptance of your very kind invitation to——
I very much regret that I cannot avail myself of the opportunity to——
I am grateful to you for your kind invitation, but——
I regret that I am unable to comply with your request because——
I regret extremely that——