Jane Hutt said the figures showed there had been improvements
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The number of patients facing long waits for some NHS treatment in Wales has risen over the past three months.
Latest figures show those waiting more than 18 months for their first outpatient appointment increased by 14% between March and June.
More are waiting over a year for inpatient treatment, but none for more than 10 months for heart surgery.
The Welsh Assembly Government said the situation had improved since last year.
The Conservatives said the figures were evidence that First Minister Rhodri Morgan and Health Minister Jane Hutt are failing hospital patients across Wales.
The number of people waiting more than a year and a half for inpatient treatment rose by 3.3% to 1,477.
Meanwhile, the number waiting more than a year rose by 5.7% to 8,940, a figure which includes patients who have declined a second offer of treatment at another hospital.
Since the end of March there has also been a rise in the number of people waiting more than 18 months for a first outpatient appointment.
It has now gone up by 14.5% to 7,105.
Ms Hutt described the figures as "encouraging" compared with the same quarter last year.
The number waiting more than 18 months for inpatient or day case surgery fell from 5,754 to 1,130, compared with the same period last year.
There were also 662 fewer people waiting more than four months for cataract surgery, and the total waiting over 18 months for orthopaedic surgery was down from 57 to two.
"There is always a difficulty between March and June with bank holidays and Easter - there tends to be a traditional increase of patients waiting," she said.
"In the areas we have targeted as priorities, there are significant successes to report."
She said that, in the last three months, 406 patients took up on a new scheme offering people the chance to be treated in a different hospital if their local hospital could not deliver treatment.
But she said the NHS still had a long way to go.
"I don't think it's good enough," she said.
"Where I feel that trusts are not taking the action we need to deliver a first-class service, I am asking our regional directors to call the chief executives in to discuss how they are going to reduce their waits."
Welsh Tory health spokesman Jonathan Morgan said the assembly government's cabinet should be "utterly ashamed".
Mr Morgan said: "It demonstrates the need for strictly targeted expenditure into the frontline services, rather than frittering money away on more quangos."
"The woeful record of this Labour government severely threatens the devolution project and I am becoming increasingly concerned at the level of public trust and belief in devolved governance thanks to Rhodri Morgan.
"It could very well be that the party credited with the establishment of devolution may very well be the party that brings the whole process crashing down, with hundreds of thousands of patients suffering."