The number of insurance applications received by America's largest state healthcare exchange has jumped by 60% this month, according to new data suggesting national website problems are gradually being eclipsed by success at a regional level.

The figures, published late on Tuesday by California, also revealed a record weekly total for people contacting the Department of Health Services by telephone to seek information on enrolment.

Though independently managed states like California, which operates its own website, have consistently out-performed the troubled federal programme, their accelerating growth rates are now giving hope to administration officials in Washington that a similar explosion in national demand may occur once their healthcare.gov site is functioning properly.

Kathleen Sebelius, health and human services secretary, this week promised officials in the 36 states reliant on healthcare.gov that the site would be operating at increased capacity in time for a self-imposed deadline for fixing its various software glitches on Saturday.

A range of problems that overshadowed its launch in October deterred all but 26,796 people from registering for health insurance through the federal exchange in its first month.

This was dwarfed by 79,391 who registered in October through 14 exchanges run independently by states like California and New York.

However, the first glimpse of comparable figures for November suggest this was not one-off demand at state level and points to month-on-month growth rates as high as 60%.

California, which uses different metrics to assess underlying demand, saw its total number of enrolment applications climb from 334,027 to 385,556 last week. Weekly application totals released by the state in November are now 60.3% above the same four week period in October, according to Guardian calculations.

Covered California, which operates the state exchange, also claimed it had received 94,000 phone calls to its service centre during the week ending November 23, the largest weekly total to date.

Similar strong growth rates have been seen in New York, Connecticut and Washington state although Oregon and Maryland have experienced glitches which mirror the national problems.

White House officials are bracing themselves for pent up demand on healthcare.gov, introducing an electronic queuing system and downplaying the significance of this weekend's deadline as they seek to manage expectations about the site's increased capacity.

But Obama pointed to the success in California as a positive signal during a trip to San Francisco and Los Angeles this week. “Thousands of Californians are signing up every day for new health care plans all across this state,” he said. "So even as we’re getting this darn website up to speed and it's getting better, states like California are proving the law works. People want the financial security of health insurance.”

Peter Lee, executive director of Covered California, says he hopes to have 70% of the state's uninsured people covered by the end of 2014 as a result of the successful launch there. “The federal government was behind because so many states at the last minute said they weren't going to play,” he told radio interviewers on Monday. “Hopefully they'll catch up.”