Police are in a tense stand-off with a man in the Newcastle suburb of Tighes Hill after a stabbing and two robberies within hours of each other in Sydney and Newcastle on Monday night.

Officers began searching for the "agitated and aggressive" man after he allegedly stabbed three people in a random attack at a gym in Brookvale, in Sydney's northern beaches, at 8pm.

It is alleged he then drove to Newcastle in a stolen car and demanded money at two service stations in Sandgate, at 9.45pm and 10pm.

Anyone who saw the man, described as having a full beard and being aged in his mid to late 20s, was advised to call triple-0.