Airport operator BAA has said recent immigration queues at Heathrow were "unacceptably" long.
Last week some passengers faced waits of two-and-a-half hours to get through immigration at the west London airport.
With thousands of athletes due to arrive at Heathrow over the next three weeks, there are concerns the immigration system - the responsibility of the Home Office - may not be able to cope.
BAA said the Home Office had promised all Border Force desks at Heathrow would be manned during the peak Olympics arrival times.
But it added that the Home Office should be "delivering a good experience for regular passengers as well as Olympic visitors".
Under its targets, the Border Force must get non-EU passport holders through immigration at Heathrow in less than 45 minutes for 95% of the time. The target for EU passport holders at Heathrow is less than 25 minutes for 95% of the time.
According to the Daily Telegraph there were half-mile queues at Heathrow's Terminal 4 last Friday, while pictures in the paper showed empty immigration desks.
A BAA spokesman said: "Immigration is a matter for the Home Office. The Home Office has said that from July 15 all Border Force desks at Heathrow will be open during peak arrival periods.
"Immigration waiting times for passengers during peak periods at Heathrow in the last few days have been unacceptably long and the Home Office should be delivering a good experience for regular passengers as well as Olympic visitors."
The Immigration Service Union, which represents 4,500 border staff, told the Daily Telegraph that the present problems were being made worse as only about half the current workers were fully trained to allow passengers from anywhere in the world entry.
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