"urgent email" is correct and usable in written English.
You can use it to refer to an email that requires immediate attention or action. For example, "I just received an urgent email from my boss; I need to take care of it right away."
Have you ever breast-fed while replying to an urgent email?
He wrote an urgent email to Mr. Howard, instructing him to meet outside the newspaper's headquarters in Manhattan.
What really distracts me when I'm writing are the concrete realities of life; doing my tax return, or that urgent email to my agent, or the school run.
The dog's owners said they had then contacted the Kennel Club by urgent email to its press office to report the dog's death and then faced a "barrage" of emails from the organisation.
He was in a graduate school class when he received an urgent email from military officials in Afghanistan and sent a specific document in response, using his personal email account, Mr. Carroll said.
Two weeks ago, after a hacking scare, the DCCC sent an urgent email to all campaigns titled "Reminder About Cybersecurity". That email included three attachments, one of them advising not to send or open email attachments.
But "urgent" emails are only the most obvious manifestation of an endemic phenomenon.
After urgent emails, Hollywood found someone who could interpret on a conference call.
I couldn't figure out if it was calendar invitations, emails, "urgent" emails, text messages, tweets or what.
I must admit, I'm not quite sure I'm ready for all those urgent emails and 5am phone calls.
Planning tweets for an event three months away may not be worthwhile when you have urgent emails to deal with.
