The White House has transferred responsibility for improving the Reagan administration's standing with women from Faith Ryan Whittlesey, chief of President Reagan's office of public liaison, to a new coordinating council on women chaired by deputy chief of staff Michael K. Deaver.

The Reagan administration's two female Cabinet members, Transportation Secretary Elizabeth Hanford Dole and Health and Human Services Secretary Margaret M. Heckler, are prominent members of the new group, which was formed two weeks ago, according to White House officials.

They said the change was made because Whittlesey, in recent White House meetings, has been the only senior official to dispute the existence of a political "gender gap"--significantly lower support for Reagan among women than among men--and the need to do something about it. One official said that Whittlesey is widely viewed in the administration as "a disaster" on women's issues.

Whittlesey said yesterday that she saw the president last week and told him: " 'Mr. President, I'm going to let you know what I'm thinking and my views on women and everything else. It's not always going to be in agreement with all the other points of view here. I think you should hear every viewpoint.' He said I had his confidence."

Whittlesey has had other disagreements with senior Reagan aides. She drew criticism for scrapping plans in March for Reagan to make a speech on the economy and business to the National Association of Manufacturers. Instead businessmen sat silently through a Reagan address on Central America.

Whittlesey, who fired most of her staff when she took office on March 2, has yet to fill a number of posts dealing with key constituencies. When Reagan tried to woo Hispanics last month with trips to Miami and San Antonio, the White House had no official liaison to Hispanic groups.

"She is a cold woman," said one senior official. "She seems to feel she has something to prove to the boys." The official said that White House communications director David R. Gergen, chief of staff James A. Baker III and presidential assistant Richard G. Darman "were on her side and fought to get her here. They want her to succeed. She has alienated every one of them with her more-conservative-than-thou style."

"I'm a practical politician like they are," responded Whittlesey, 44, who has been a county commissioner in Pennsylvania and ambassador to Switzerland. She said she plans to fill her staff next week with new appointments that would include blacks and Hispanics.

"It's frustrating at times," she said describing her job. "It's a lot of hard work and then there is what I call creative communication, leaks to newspapers . . . .

"I am the only woman in the White House senior staff meeting, and that's a group of 18," she added. "Institutional attitudes change slowly, and that's not only at the White House. It's every institution in life . . . I've lived all my life in a male-dominated world."