Apple announced a first-quarter profit of $1.61 billion and sales of $10.17 billion, both records for the company, led by continued fanfare for its iPhone, iPod music player and Macintosh computers.

Profit in the first quarter last year was $1.58 billion, while revenue was $9.6 billion.

However, Apple only sold 4.36 million iPhones, much less than the 6.9 million sold in the previous quarter.  Apple also sold 22.73 million iPods and 2.52 million computers.

“Even in these economically challenging times, we are incredibly pleased to report our best quarterly revenue and earnings in Apple history,” CEO Steve Jobs said.

Jobs himself is an extremely relevant factor to Apple’s results. The celebrity CEO recently announced health issues that will keep him away from day-to-day management until the end of June.

For the second quarter, Apple expects revenue of $7.6 billion to $8 billion, CFO Peter Oppenheimer said.