DULLES, Va. — A top aide to Mitt Romney said that the campaign had obtained “several years” of income tax returns from potential running mates – suggesting that Representative Paul D. Ryan had produced tax returns for a greater number of years than Mr. Romney has in his run for the White House.

Mitt Romney has repeatedly refused to disclose tax returns for any years but 2010 and 2011, stirring criticism that he is shielding his finances from public view.

But on Saturday, the Romney adviser who oversaw the vice-presidential search, Beth Myers, said that she had requested “several years” of returns from Mr. Ryan. When pressed on precisely how many she had received, she declined to elaborate.

But her choice of words, however vague, was telling: she said “several,” not two, or a couple. (Technically, several refers to more than two.)

President Obama’s re-election campaign has hammered Mr. Romney for not releasing enough of his tax returns, attempting to portray him as a calculating businessman set on hiding his wealth and tax rate. Because Mr. Romney earned much of his money through something known as carried interest – a form of return on investments – when at Bain Capital, he paid a lower tax rate than he might have had he worked in a different profession.

Mr. Romney has said that releasing two years of tax returns is plenty and that he is following a precedent set by presidential candidates like Senator John McCain in 2008.

Mr. Romney’s own father, however, released 12 years of tax returns when he was considering a run for president in 1967. And in 2008, Mr. Romney himself gave Mr. McCain 23 years of his tax returns when being vetted as a possible running mate.