President Carter, acknowledging that "controversy has swirled around the White House" ever since his inauguration, appealed yesterday for his party's support on the Panama Canal treaties and other high-priority foreign and domestic goals on Capitol Hill.

Appearing before the Democratic National Committee for the first time since taking office, Carter conceded that Senate approval of the canal treaties "is in doubt," and that several legislative proposals, including the energy package, are facing formidable opposition.

He bluntly told the Democratic leadership that on the volatile question of ratification of the Panama treaties, "I need your help . . . The matter is in doubt."

But Carter said he welcomed controversy because he views it not as a sign of weakness or failure but as evidence that his administration is at least trying to fulfill the promises he made in the 1976 presidential campaign.

In a wide-ranging speech that touched on most topical domestic controversies and a diverse array of foreign policy issues, Carter seemed to be making a rare - for him - bid for party unity in behalf of his program.

"I want to be a good President. With your help, I can be a good President. But I also want to be a good Democratic President," Carter said.

In his first 10 months in office, Carter has made few references to himself as a Democrat, or to his policies in the context of furthering the Democratic Party tradition, leading to conjecture that he is disinterested in party business.

But in his 25-minute speech, he made a personal appeal to the national committee to limit the size and the cost of the party's 1978 mini-convention, a request that was heeded later despite an attempt by liberals to nearly double the number of delegates in order to give broader grassroots and minority representation.

Of his most vulnerable domestic program - the energy package that is being dismantled piecemeal in the Senate - Carter said. "It is not easy. The shadow of the oil lobby hovers over Capitol Hill."

Saying that Senate Majority Leader Robert C. Byrd (W.Va.) is "doing the best he can" to steer the package through the Senate. Carter promises "What we don't get this year, I will be back next year again. I don't intend to fail, because the people need it."

He vigorously defended his welfare and tax revision programs, his government reorganization proposals and his attempts to reduce unemployment, saying that the controversy over some of these policies was inevitable.

"Many of the issues we are now approaching strongly and boldly and for the best interests of the American people have been avoided for years, for decades, for generations because of a fear of arousing controversy and open debate, but they can't be avoided any longer and I have no inclination to do so," the President said.

Turning to his foreign policy, Carter defended the joint U.S.-Soviet Union statement on the Middle East, which has infuriated many of Israel's supporters. He called it "an achievement of unprecedented significance" and a "crucial element" of the upcoming negotiations at Geneva.

The Soviet Union, Carter said, has become "much more moderate" in its position toward Israel, and the joint statement, while not a prerequisite to a Middle East settlement, is a "sound step forward."

On the canal issue, Carter urged the Democrats to help him gain Senate approval of the two treaties that would give Panama full control of the waterway in the year 2000.

Signing the treaties, Carter said, signaled the emergence of a new relationship with Latin American nations, and an "affirmation of mutual purpose, an end of colonialism that is profound."

In an apparent response to disclosures that U.S. negotiators are opening new talks with the Panamanians because of difference in interpretation on the United States' future rights to intervene militarily and obtain priority passage of warships in times of conflict, Carter declared:

"We retain the right to defend . . . to operate and manage the canal throughout this century - 23 more years - and after the year 2000 to ensure that the canal will open for all commerce and neutrality guaranteed."

Carter was followed to the lectern by Ellsworth Bunker, one of the special U.S. ambassadors who negotiated the treaties, who gave the committee members a briefing on the documents' provisions.

Bunker said rejection of the treaties would be a "stunning blow" to U.S. and Latin America relations, and pledged that this nation's right to maintain neutrality in panama is "unlimited."

The Democratic National Committee then adopted a resolution supporting the President in "the ratification process" and proclaiming support of the treaty negotiations conducted by Carter.

But the resolution was slightly watered down from an earlier draft approved by the DNC executive committee, which "proudly proclaimed its full endorsement and warm support" for the treaties themselves. The stronger version, which failed to win endorsement by the party's resolutions committee, also urged approval by the Senate.

While Democratic National Chairman Kenneth M. Curtis said he felt both drafts showed the party is "100 per cent behind the President," other party leaders said the broader language was adopted to be more palatable to some southern Democrats who did not want to be on record favoring ratification.