pressing demand; relentless urging; insistent request
Describes a situation where someone is being strongly and repeatedly urged to do something, often with a sense of urgency or pressure. The phrase is a set expression and not used as a standalone noun in the same way as 催促 alone.
We were pressed relentlessly by the client and had no choice but to move up the delivery date.
He was hounded for repayment of his debts and couldn't sleep at night.