Still more statements by President Reagan at his Tuesday news conference were disputed yesterday, these on Pope John Paul II and on an Arizona program to aid the elderly.

Earlier there had been disputes over his misstatement of several unemployment statistics.

The president said that the pope had written him a letter expressing approval of the actions Reagan has taken in response to the imposition of martial law in Poland. But Vatican officials said in a statement issued Wednesday that the pope's letter was not intended to be political or to express approval for any specific action.

White House communications director David Gergen told reporters yesterday that Reagan stands by his characterization of the letter. Gergen said he had read the 3 1/2-page letter yesterday. It was dated Jan. 4 and was written in response to letters Reagan sent to the pope.

In his news conference and, at greater length in a speech in New York last Thursday, Reagan praised a Pima County, Ariz., program that feeds elderly poor people for cutting costs while simultaneously doubling the number of persons it aided.

However, reporters found that the only reason people were working for the program as volunteers rather than on salary was that federal grant money had run out and they were waiting for new funds before going back on the payroll. The increase in people being fed resulted from the closure of other government sponsored facilities.

Gergen said the White house learned of the feeding program when one of its officials wrote to Office of Management and Budget deputy director Ed Harper in October. He added that a White House researcher telephoned the program to check its claims before Reagan delivered his New York speech.

Gergen said the White House had made "a good faith effort" to check the facts.