The White House is "really sorry." Some 1,200 women from 56 countries meeting in Washington are "furious" and "insulted." And the so-called "gender gap," that potentially lethal chasm in the polls showing that women are less likely than men to support President Reagan, may have inched a bit wider.

The cause of it all was a special tour of the presidential mansion that ended yesterday afternoon at the East Gate of the White House before it even began.

Due to a scheduling error--"a little mistake that had a colossal impact," said a White House spokesman--1,200 members of the International Federation of Business and Professional Women's Clubs were turned away from a tour planned by the clubs for more than a year.

"I'm furious, absolutely furious," said Polly Madenwald of Hillsboro, Ore., president of the United States branch of the organization that represents 206,000 women worldwide and is gathered this week in Washington for an international congress.

"We consider it an international incident," said Madenwald. "I believe it was a slight to us, and I'll tell you, the gender gap is rapidly getting wider and wider. We spent $1,800 for buses to take members to the White House for the tour ."

President Reagan was "particularly upset" when he heard about the mix-up late yesterday afternoon, according to White House spokesman Anson Franklin. Reagan telephoned Madenwald at 5:50 p.m., apologized and ordered his schedule changed so that he could speak to the group today, Franklin said.

The White House said last night that the president would address the group at 10 a.m. today at the Sheraton-Washington Hotel.

Six chartered buses filled with BPW members showed up at 2 p.m. yesterday at the East Gate where Madenwald said she was told that the tour "wasn't on the schedule."

"I said, 'I have it in writing,' " Madenwald recalled, referring to a letter she received in July confirming the tour.

"Nobody notified me. Nobody notified our staff here . . . The largest and oldest working women's organization in the United States has been totally embarrassed by the administration," Madenwald said, in remarks made before Reagan called her.

At the White House late yesterday afternoon an aide explained that the mix-up apparently was caused when the president hastily arranged a briefing on government management reform in the East Room and "nobody got to the tour group" to tell the members that their tour had been canceled by that event.

Faith Ryan Whittlesey, an assistant to the president who deals with women's issues, had met with a group of BPW leaders early yesterday morning.

Later that day, after she heard that the buses had been turned away, Whittlesey said she called Madenwald, said she was "really sorry" and tried to arrange another tour of the White House for today. Because the organization had scheduled a full day of meetings for Wednesday, a substitute tour could not be arranged. Within three hours the president ordered his schedule changed.

"It was a failure that has everyone very concerned over here at the White House," said Franklin.