RENO, Nev. (AP) _ President Reagan claimed Tuesday that candidate George Bush and the Republican Party espouse the policies and ''traditional values'' of the great Democratic presidents Franklin Delano Roosevelt, Harry Truman and John F. Kennedy.

Hopping on the name-game bandwagon of Bush and his running mate Dan Quayle, Reagan campaigned in Nevada and in his home state of California, assailing Democratic candidate Michael Dukakis for acknowledging earlier this week that he was ''a liberal'' in the tradition of FDR, Truman and Kennedy.

Reagan contended that the Democratic candidate ''is no Harry Truman, and he's no FDR,'' tagging Bush's rival with the ''Carter-Mondale liberal agenda'' of high taxes and big government.

''The opposition, even after finally admitting their liberalism, is still trying to deny that they've left the mainstream behind, and now belong to the party of (Sen. George) McGovern and (former vice president Walter) Mondale - that's the type of liberals they are,'' Reagan said.

''No, the fact is that today, if you want America to be what FDR called a 'great arsenal of democracy,' if, like Harry Truman, you want to continue to help those resisting communism, if you believe in lowering tax rates like John F. Kennedy did, and in the traditional values that you grew up with, then you should vote for our Republican ticket, because that's what we believe in, and the self-proclaimed liberals don't,'' Reagan asserted.

For weeks, Reagan and Bush have clubbed Dukakis with the 'liberal'' tag, insisting it carries with it policies of big government and high taxes, instead of the more traditional image of personal liberty and resistance to absolute government.

The president also poked fun at Dukakis' populist slogan, 'I'm on your side,' saying:

''The liberals now are saying that they're on your side. I guess they think that that will make it easier for them to reach their hand around and put it in your pocket.''

Reagan's comments came in remarks delivered at a rally on behalf of Sen. Chic Hecht, R-Nev., locked in a neck-and-neck race with the state's popular Democratic Gov. Richard H. Bryan.

At the airport rally, Reagan shared billing with a live elephant named Bertha, who carried a sign saying ''Stick with Chic.'' The elephant regularly performs at the Nugget, a hotel and casino in the Reno area.

The rally, within sight of the foothills of the Sierra Nevada mountains, began under a light cloud cover, but the sun broke through the clouds as Hecht was introducing the president.

Reagan told his Nevada audience that ''there will be two Democratic governors who want to go to Washington'' on the ballot this year, dubbing Dukakis and Bryan, ''the tax and spend twins.''

The president put in a plug for the staunchly conservative Hecht, who has suffered from an image problem due to sometimes awkard oratorical habits, but pulled lately within striking distance of Bryan.

''Chic doesn't grab headlines, he doesn't showboat. Chic's the kind of senator who doesn't make a lot of noise. He just gets things done for his state,'' Reagan said, pointing in particular to Hecht's work on behalf of raising the 55 mph speed limit to 65 mph.

Nevadam with its four electoral votes, is firmly in the Bush camp.

According to published reports, both Bryan and Hecht planned to spend at least $2.5 million in their hard-fought contest, which pits Hecht, a former banker and clothing store owners, against Bryan, a highly rated state official.

Earlier in the day, Reagan took a final campaign bow in his home state of California.

Seeking votes to clinch the state for the vice president, Reagan tried to churn up votes in arch-conservative Orange County at an exhuberant student rally at the local California State University-Fullerton campus.

''Don't be fooled, folks, George Bush's opponent is no Harry Truman, and he's no FDR,'' Reagan said.

''Yes, it's the same Carter-Mondale liberal agenda they're pushing - less defense, more big government,'' Reagan said, referring to former President Jimmy Carter and his vice president, Walter Mondale, the man Reagan defeated in the 1980 landslide election.

The president also stoppd in middle class San Bernadino, where he spoke at a state GOP rally near the famed Riverside auto racetrack.

Reagan planned to travel on Tuesday evening to Milwaukee, where is he scheduled to add his prestige to the Senate campaign of Susan Engeleiter, Republican leader of the Wisconsin state Senate. Public opinion polls show Mrs. Engeleiter trailing behind Herbert Kohl, the owner of the Milwaukee Bucks basketball team.

Before returning to Washington, the president will campaign in another battleground state, Ohio, appearing at Baldwin-Wallace College near Cleveland.