The company's pre-tax profit fell 4.5% to £16.5m for the six months to June 30 - down from £17.3m for the same period last year.
Greggs said tough trading conditions and the wet weather kept customers away and it expects business will continue to be tested.
It added that industry expectations for food ingredient prices to go up across the globe would likely affect consumers.
The company said: "The market remained challenging and was particularly impacted by the record levels of rainfall in the second quarter with UK high street footfall down over 7%."
"Greggs was not immune to this and our like-for-like sales fell by 3.5% in the second quarter and by 2.3% in the first half overall."
It comes after the bakery successfully campaigned against the Government's plans to introduce a pasty tax earlier this year.
Chancellor George Osborne scrapped proposals to charge 20% VAT on hot pasties and sausage rolls after Greggs chief executive Ken McMeikan marched on Downing Street to deliver a 300,000-strong petition.
Mr McMeikan said: "There's no question that the profile of Greggs is significantly higher than it was before the pasty tax started.
"But we were not able to see how much that has benefited sales - the Chancellor announced the tax in March but in April it started raining and didn't stop."
He added: "This really is a very resilient performance, given the exceptional weather."
Despite the profit slump, the company has opened 33 new outlets this year which helped push total sales up 4.5% to £350m.
It says it is on track to open a record 90 shops in 2012.
The group also reported weekly like-for-like sales in its London stores were up 10%, since the Olympics began.
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