Chief executive Stuart Gulliver said the industry was moving into "calmer waters" in the wake of the credit crunch and the PPI mis-selling scandal as charges for bad loans and compensation fell.
But Mr Gulliver, who was paid £7.4 million last year, said he could not give any assurances over potential future job losses.
Underlying profits in the first quarter of 2013 were up to 7.6 billion US dollars (£4.9 billion), from 5.7 billion US dollars (£3.7 billion) - representing a 34% year-on-year rise.
Worldwide, the bank has lost 40,000 of its 300,000 employees as a result of restructuring and sell-offs since Mr Gulliver took over at the start of 2011. The cuts are 10,000 more than the number predicted at the time. Mr Gulliver said HSBC was responding to "economic and regulatory" circumstances.
The bank, which is due to give a key strategy update next week, expects total staff numbers to fall eventually to 254,000.
The bank said its improved profits for the first quarter of the year reflected higher revenues and lower loan impairment charges, with a notable improvement in its US consumer and mortgage lending business.
Its UK customer redress programme, which includes compensation for PPI as well as card and identity protection insurance policies, was 164 million US dollars (£106 million) in the first quarter, compared to 286 billion US dollars (£184 million) in the last three months of 2012. The figure shows that the pot of money set aside to reimburse customers is still swelling but at a reduced rate.
With loan impairment charges - losses from bad debts - also falling, it suggests HSBC is beginning to overcome the difficulties of the credit crunch and the mis-selling claims that have dogged the industry over the last few years. Mr Gulliver said: "As an industry, we are moving into calmer waters but I don't think it is time to reduce the vigilance that we need to demonstrate."