expression
by your leave; with your permission
A formal, self-deprecating phrase used to preface a remark or action that might be presumptuous, often in speeches or formal writing.
僭越ながら、一言ご挨拶を申し上げます。
By your leave, I would like to say a few words of greeting.
僭越ながら、私からも意見を述べさせていただきます。
With your permission, I would also like to express my opinion.
From 僭越 (presumptuous, audacious) + ながら (while, though). The phrase literally means 'though it is presumptuous of me'.