Cuyahoga County Democratic Chairman Timothy Hagan, faced with growing opposition within his party, today withdrew his support of efforts to draft Sen. Edward M. Kennedy (D-Mass.) for the 1980 presidential race.

Although he had been a catalyst for a proposed draft-Kennedy resolution to be offered at the county party's central committee convention here Saturday, Hagan said he changed his mind about the draft after meeting in Washington today with former Ohio governor Michael V. DiSalle.

"My ardor for the resolution has cooled," Hagan said after being persuaded by DiSalle that the resolution was inappropriate and would be awkward for Kennedy, who has disassociated himself from the draft movement while declaring his support for President Carter.

DiSalle, a Washington lawyer who remains active in party affairs, invited Hagan to his office today to discourage the Cuyahoga County Democrats' plans.

"People are getting the idea that he [Kennedy] is promoting the draft, and he's not," DiSallee said. "So there's no need to draft him. In the end, you'll have a reluctant candidate."

DiSalle said he wasn't acting as an intermediary for either Kennedy or Carter, but was responding to a request from an Ohio friend, whom he did not identify.

"I've known the Kennedys for a long time," DiSalle said. "And I got a call from Ohio saying that if I could call Hagan and have him stop this thing it would be something the Kennedy people would like."

A Kennedy aide had asked Hagan earlier to scuttle the draft efforts, but Hagan said he had not heard from the senator.

Several key Democrats in Ohio, including Paul Tipps, the party's state chairman, and Sen. John H. Glenn Jr., have spoken out against a Kennedy draft, saying it would split the party. They have noted that Kennedy has repeatedly said he is not a candidate.

Hagan said he couldn't predict whether the resolution would still be offered at Saturday's meeting by other Kennedy loyalists here, but he said he was now prepared to oppose it.

City Council Clerk Mercedes Cotner, who was to have introduced the resolution, said she was surprised by Hagan's decision and might still press for the Kennedy draft at the party meeting.