The head of the union whose members process the millions of tax returns mailed last night has blamed staff reductions for this year's Internal Revenue Service refund delays.

"The time bomb of too many tax returns and too few resources has caught up with the Reagan administration and has exploded," Robert M. Tobias, president of the National Treasury Employees Union, said yesterday. "America has just witnessed the most disastrous income-tax processing season in history."

But IRS figures released yesterday show that the service is catching up rapidly on its backlog. Although fewer returns have been processed nationwide than at this time last year, the IRS's 10 regional centers together have processed record numbers of returns in the last two weeks. Officials say the new, $103 million computer system responsible for the delays has been running better.

During the week ended April 12, the IRS processed 51 percent more returns than it did during the same week in 1984: 7.2 million returns compared with 4.8 million last year. In the week ended April 5, 25.2 percent more returns went through the system than in the same week in 1984.

Cumulatively, the service remains behind, having processed 13.4 percent fewer returns so far during this filing season than in the same period in 1984. But that's an improvement from February, when the IRS was running as much as 59 percent behind.

Both of the centers that handle Washington-area returns were still behind overall. The Philadelphia service center, where returns from the District and Maryland are sent, has processed 2.3 million returns, 60 percent of the number it had completed by the same time in 1984. The Memphis center, which handles Virginia returns, has completed 4.9 million returns, 83 percent of last year's total. Both have improved their processing speed this month.

"The last weeks have been just tremendous," said IRS spokesman Larry Batdorf.

Tobias, however, predicted more IRS errors, more taxpayer complaints, fewer audits and a decline in collections as a result of personnel cutbacks for budgetary reasons. While the number of individual and corporate returns has risen since 1980 by 37 million, 5,900 positions have been cut from the IRS payroll of 86,000, he said.

He recommended the hiring of 5,000 more people in the areas of return-processing, tax examination, investigation, collections and taxpayer service. Those additions would raise tax revenue by $2.7 billion in the first year, he said, at a cost of $174 million, not including training costs.

The administration has proposed hiring 7,500 more auditors over three years, but the process would not begin until fiscal 1987. In other areas, such as taxpayer service, the administration wants to continue cutting personnel.

Office of Management and Budget spokesman Edwin L. Dale Jr. said the IRS budget as a whole has risen by 42 percent in the last four years, or 14 percent after adjustment for inflation. Staffing has declined, however, as a result of computerization and automation, he said.

Roughly 100 million returns were expected to be sent to the IRS before midnight Monday, a large majority of them requesting refunds. Commissioner Roscoe L. Egger Jr. has said he expects the service will meet the June 1 refund deadline, after which interest must be paid on late refunds, for all returns except those that are particularly difficult to process.