Letter volumes fell 4% in the six months to the end of September but the fall was offset by a 4% rise in parcel volumes.
Royal Mail reported adjusted pre-tax profit of £240m against £287m a year earlier.
It said performance for the full financial year would depend on Christmas - its busiest time of year.
Royal Mail said its "transformation costs" increased by £47m in the period with some 3,000 staff opting to take voluntary redundancy.
It said the total cost of restructuring the business this year was likely to be at least £180m.
The rise in the number of parcels came as a result of gaining new customers, Royal Mail said.
But despite the increase in parcel volumes, revenues from Royal Mail's UK parcels business - which includes its letters division - dipped 1% in the period.
The fall in UK parcel revenues however was offset by an 8% rise in revenues across the rest of Europe.
Although letter volumes continued to fall, the 4% drop in volumes in the six months to the end of September was at the lower end of the range forecast by Royal Mail.
Shares in Royal Mail rose 5.8% to 480.5p in early trade. Its shares were boosted because the 2% fall in underlying operating profits to £342m - Royal Mail's preferred profit measure - was less than expected, and the firm also said UK operating costs would be "at least" 1% lower this year.
Moya Greene, chief executive of Royal Mail said the company had delivered a "resilient performance" in what she described as a "competitive trading environment".
The half-year results are the first to be published by Royal Mail as a completely privatised company after the government sold its remaining shares in the business last month.
Royal Mail increased its half-year dividend payment to shareholders to 7p per share from 6.7p per share a year ago.
Royal Mail said little about the review of the way in which it was regulated, announced by communications regulator Ofcom in June, other than to say it had submitted its response to the review in September and agreed there was a need to consider the effectiveness of the existing regulatory framework.
Ofcom has said the review is expected to be completed and a revised regulatory framework in place during 2016.
Royal Mail has reported a near 15% fall in half-year profits with revenues little-changed across its business.