"But having met with the pathologists and other medical personnel, there is sufficient information to continue a full investigation into the circumstances of Mr Woolmer's death which is now being treated as suspicious."
'Murder plot' stories
Asked if Jamaican police were pursuing a murder investigation, Shield said: "No, we are not saying that," but did not specifically state that murder had been ruled out.
The news conference in Jamaica was called after reports emerged in Pakistan's print and electronic media of a possible murder plot.
Police said that further tests, including toxicology and tissue analysis, would be carried out.
Woolmer, 58, died in hospital on Sunday after being found unconscious in his hotel room in Kingston.
His death came a day after Pakistan, the former world champions, had been knocked out of the World Cup by Ireland.
Mushtaq Ahmed, the former Pakistan international leg-spinner who was due to take charge of the team for Wednesday's game against Zimbabwe, said the squad was having a hard time coming to terms with the tragedy.
"There is a great vacuum because Bob was a part of the family," he said. "When you lose a member of the family, we all know how bad it can be. The whole team is depressed right now."
The Pakistani players have said they want to win their final World Cup match for Woolmer.
Inzamam-ul-Haq, who announced his resignation as captain and retirement from one-day cricket following Woolmer's death, said the team owed Woolmer a victory.
"We'll do our best for Bob, but whatever we do, it won't be enough," the 37-year-old batsman said. "He was a good man. Whenever any of the boys had a problem, he'd sit with them, and we were very attached to him."
"He was a very good coach and human being. Because of this, he had a lot of respect from the team. He was brave and knew how to handle the situation when everybody was feeling down. He will be well remembered."