Pathology services that have been affected since September 18 include blood bank and transfusion, haematology, biochemistry and microbiology.
But the NHS trust said it hopes to have “full functionality restored” and be “back to normal clinical practice” by the end of this week.
Most services are continuing as normal today now that a backlog in primary and secondary care has been cleared. On Friday, 8,000-10,000 blood tests had accumulated in the system which needed to be processed.
GPs can now request routine blood tests and receive results as normal.
Inpatient, day case and outpatient appointments at Leeds Teaching Hospitals should also continue as normal from today.
The blood transfusion system has been restored and the blood sciences system should be fixed by tomorrow.
The NHS trust’s chief executive Julian Hartley has written to patients affected by the problems to apologise.
Suzanne Hinchliffe, chief nurse and deputy chief executive at Leeds Teaching Hospitals said: “We have made good progress over the weekend in addressing the serious issues affecting our ability to deliver a full pathology service.
“Our teams have been working hard with internal and external partners to resolve the IT issues and we have also put in place temporary arrangements for alternative testing to minimise the impact on patient care.
“We have processed all known requests and there is now no backlog for both primary and secondary care.
She said that as of Friday arrangements were made for Bradford Teaching Hospitals to be able to carry out tests. It has initially also suffered problems with its pathology IT system.
GPs can request routine blood tests and receive results as normal, she added.
“With the additional contingency arrangements we have put in place, inpatient, day case and outpatient appointments at Leeds Teaching Hospitals will resume as normal.
“I would like to apologise to everyone for the inconvenience these problems have caused.
“We recognise that it is taking a significant time to restore the IT system but this is a very complex issue.
“We have already restored our blood transfusion system and this is now operating as normal and we continue to work on our blood sciences systems with some being ready for testing by Wednesday.
“Throughout this issue, patient safety has been our main priority and to date and we have continued to provide urgent, emergency and cancer procedures.
“Unfortunately we have had to postpone 113 patients’ operations as a result of the issue with the pathology IT system.
“We recognise the inconvenience and upset this causes for patients and for this we are very sorry.
“We hope to have full functionality restored and back to normal clinical practice by the end of the week.
“We have made general information available to patients and the public using our website and clinical staff have contacted patients who are affected directly to explain the situation, apologise and make alternative arrangements.
“Our Chief Executive, Julian Hartley, has been closely involved in resolving the issues and has been speaking to staff and patients; liaising with partners, suppliers and our own teams to ensure a collaborative system-wide approach.
“He has given his personal apologies in a letter to patients affected by this issue.”