WASHINGTON — Hospitals are making little progress in reducing the frequency at which Medicare patients are readmitted, despite a government campaign and threat of financial penalties, according to newly released government data.

The US government and health policy experts consider frequent readmissions a sign of the shortcomings in the health care system, with one in five Medicare patients returning to the hospital within a month of discharge.

In October, Medicare will begin to penalize hospitals with higher than expected readmission rates as required by the 2010 federal health care law.

‘‘We’ve put all of this policy effort into this area, and yet we’re seeing no movement,’’ said Ashish Jha, a Harvard School of Public Health professor. ‘‘Either we have no idea how to really improve readmissions, or most of the readmissions are not preventable and the efforts being put on it are not useful.’’

Many hospitals have been trying new approaches to ensure that released patients get follow-up checkups, medications, and doctor’s appointments to keep them from being hospitalized again. But the industry and some experts have been critical of Medicare, saying it is not considering that some patients are intentionally readmitted or return to the hospital for unrelated ailments.

Medicare calculates readmission rates in three-year periods. The most recent rates are based on readmissions from July 2008 to the end of June 2011.

Nancy Foster, a vice president at the American Hospital Association, said the new readmission figures minimize improvements that hospitals made in 2011, since they also include two years of earlier readmissions.