Sen. Bob Dole (R-Kan.) has ended his relationship with the political consulting firm that was handling his bid for the Republician presidential nomination, but is not dropping out of the race, aides said yesterday.

Rumors that Dole, the 1976 GOP vice presidential nominee, might soon terminate his 1980 bid began circulating this week with reports that he was splitting with the Response Marketing Group, a Washington, D.C., and Tennessee consulting firm.

Dole aide Bob Waite confirmed that the original contract, expiring Sept. 1, would not be renewed, but said Tom Bell, head of the firm, was working with Dole "to find out management for the campaign."

In the meantime, he said, Bill Russo, the deputy political director of the 1976 Ford for President campaign, who joined Dole a few weeks ago as political director, will be in charge of the Dole effort.

Dole, according to Russo, "has not raised as much money as we had projected," but has pledges that will enable him to meet his original campaign budget.

His mid-year finance report showed receipts of $253,286 and expenditures of $220,217 -- substantially less than his major competitors reported. At least one-third of the money spent went to or through the Bell organization.

Waite and Russo said Dole would be campaigning all but two days this month, concentrating on six target states -- Iowa, Minnesota, New Hampshire, Massachusetts, Florida and Alabama.

Waite said there had been layoffs in Dole's campaign headquarters staff, but that the field staff had been expanded. Russo said one recent addition was Jerry Mursener, the executive director of the Iowa Republican Party, who will handle the Midwest states for Dole.