Mr Sissling insisted 94% of surgeries offer appointments at least twice a week after "normal hours".
GPs in England will no longer have to offer appointments lasting at least 10 minutes under changes agreed with the government.
Ms Griffiths said the number of GP practices closing for half a day will be reduced by April next year, and more practices will be "required" to offer appointments early in the morning or towards the end of the day.
Doctors have been told they will not need to offer appointments outside office hours and at the weekend if there is no demand for it, after the BMA expressed concern about forcing GPs to work on Saturdays.
Health Secretary Jeremy Hunt said: "We live in a 24/7 society, and we need GPs to find new ways of working so they can offer appointments at times that suit hard-working people".
Discussed in The Atlantic, research shows that psychotherapists, for example, are more likely to offer appointments to middle-class white people than to middle-class African-Americans or working-class people of any race.
For example, many practices do not offer appointments between late morning and mid-afternoon, but some patients may find such times preferable.
3 In April 2014, the UK Department of Health revealed the details of a pilot scheme that will see 1147 general practices in England, with approximately 7.5 million registered patients, begin to offer appointments outside of current opening hours.
Massage schools may only offer appointments periodically and are sometimes booked quickly.
Similarly, other therapists said that they have offered appointment books and other documents to support their bills, and that Oxford has shown no interest in seeing them.
