President Carter took the offensive against Ronald Reagan on the debate issue last night and strongly appealed to Democratic Party contributors to help him turn back what he said is the "relatively dismal future" Reagan's election would mean for the country.

Speaking to about 800 people at a $1,000-a-plate Democratic National Committee fund-raising dinner at the Washington Hilton hotel, Carter poked fun at Reagan's hollywood background and chided the Republican nominee over the negotiations to arrange a debate between the two major party presidential candidates.

"It's a travesty to know that it has not been possible to arrange it [a Carter-Reagan debate] when it is needed," the president said.

Carter refused to participate in a three-way debate with Reagan and independent presidential candidate John B. Anderson in Baltimore Sept. 21. But Reagan has refused several invitations to debate alone with the president, and his latest rejection of such an invitation from the League of Women Voters has given the Carter campaign the chance to seize the initiative on the issue.

Carter spoke briefly at the end of the fund-raising dinner and there was little emotion in his voice. But the basis of his appeal was emotional as he reminded the Democrats of the 1968 election, when he said the late Hubert H. Humphrey was defeated by former President RICHARD M. Nixon because not enough Democrats worked for a Humphrey victory.

Asserting that what is at stake in the 1980 election is nothing less than "the character of the future of our nation and the opportunity or absence of opportunity your children might have," the president appealed to the dinner audience for more than contributions.

He suggested indirectly that a Reagan victory could mean "the alienation of black from white. Christian from Jew, rich from poor and North from South," and said he needed the active support of Democrats in a number of the states where the race between him and the Republican nominee is close.

"Will you help me?" the president said in concluding the speech.

Carter also portrayed Reagan as a "muzzled" candidate who was led around by his senior advisors.

"He has his own version of the Rose Garden aproach," he said of the Reagan campaign. "There's just one item he overlooked -- he doesn't have a Rose Garden. And we are going to see to it that he never does." CAPTION: Picture, Carters and Mondales wave to crowd of about 800 at a $1,000-a-plate fund-raising dinner here last night. AP