I am following up on our conversation yesterday.
'Seguito' = SE-gwi-to; the 'ui' is a quick glide, not two separate vowels.
Use at the start of an email to remind the recipient of a prior conversation and show that you are acting on it promptly.
'Fare seguito' is the formal Italian way to say 'to follow up'. It is far more common in Italian business writing than the borrowed English term 'follow-up', though that is starting to appear in startup contexts. It implies continuity and reliability.
Come concordato ieri, le invio...
As agreed yesterday, I am sending you...
Assumes something was agreed; more assertive
In seguito alla nostra riunione di martedì,
Following our meeting on Tuesday,
References a meeting rather than a conversation
Do seguito alla mia email del [data],
I am following up on my email of [date],
When chasing a reply to a previous email
Italians value personal relationships in business, so referencing a previous conversation (even a brief one) signals that you were paying attention and take the relationship seriously.