to the effect

Preposition

with more or less the meaning of

Japanese Meaning

おおむね～という意味で / ほぼ同じ意味で / 概ね～を意味する

He sent an email to the effect that the meeting would be postponed.

彼は会議が延期されるという趣旨のメールを送った。

Sense（1）

with more or less the meaning of

He was vague but said something to the effect that he'd do it soon.