Jonathan Coulter said the recent rise in Covid cases and a lack of available care services meant patients were staying in hospital longer than they should.
He added this was having an impact on A&E waiting times which "remain below the standard we would want", with over a quarter of patients waiting more than four hours to be seen.
"We are now in mid-July, and the acute pressures, the bed occupancy, the community services workload are all greater than you would often experience in mid-January," Mr Coulter said in a report.
"During the month of June and into July, we have experienced a significant spike in people in hospital who are Covid positive.
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"We have currently over 35 people in hospital with Covid, and whilst the severity of the illness is reduced due to vaccine uptake, the infection control measures that we have had in place result in flow through the hospital being more difficult."
Mr Coulter said Covid was also having an impact on staffing levels, with around 80 staff currently off work after absences climbed above 130 in June.
He described the pressures on the wider health and care system as "enormous" and said the problem of bed blocking - where patients are medically fit to be discharged from hospital but have no care packages available - needed to be addressed.
He said: "We continue to have a significant number of patients who are medically fit within hospital, our length of stay has increased, and we have many times more patients in hospital over 14 days and 21 days than we ever had before the pandemic.
"This reflects the pressure in care services out of hospital, and we are discussing across the system how we can reduce this risk.
"We know that if people stay in hospital for a significant time that outcomes deteriorate, and we are currently at risk of worsening care for our population as a result of some of the urgent care pathway pressures being felt across all organisations."
Mr Coulter added the hospital was continuing to take ambulance patients from outside the Harrogate district and that while this was creating added pressure, it was "absolutely the right response".
He said: "Despite the pressures locally, we continue to offer significant support to colleagues in other parts of our system, in particular York Trust.
"During June, in line with previous months, we had numerous ambulances diverted to the Harrogate site, which resulted in on average around 15 additional beds occupied by patients admitted as a result.
"This is absolutely the right response to system support, but we need to recognise the impact upon our colleagues who have to organise and arrange this care."
By Jacob Webster, Local Democracy Reporter