President Carter apparently doesn't share the view of City Council Chairman Arrington Dixon that Dixon's job is as important as that of the mayor.

Dixon reportedly was miffed when the president invited Mayor Marion S. Barry to the Oval Office on Jan. 11, and tried to wrangle an invitation for himself, asserting that under the Home Rule charter, his job was as important as the mayor's.

But the word was sent back to the District Building that the president "didn't want to deal with a number of players on a number of issues," a White House aide said yesterday.

The aide said that Carter "made it very clear that we want to work with him (Dixon), but the president feels he has a special obligation to the mayor."

White House staffers, recognizing that "there may be some problem" growing out of a political rivalry between Barry and Dixon decided to invite Dixon to another meeting in the West Wing that same day, with Vice President Mondale and top White House aides, including Budget Director James T. McIntyre Jr. and domestic policy adviser Stuart E. Eisenstate.

But tit-for-tat, Dixon snubbed that meeting.

Recalling the incident yesterday, Dixon laughed off its significance.

He didn't go to the meeting with the vice president, he said, "because when I go, I'd like to go with my colleagues, so that we can express the collective concerns of the city.

"I intend to go as a representative of the co-equal branch of government" the chairman emphasized.

While acknowledging that "I was not invited," to that initial meeting, Dixon said "the mayor indicated he wanted me to go" but there wasn't time to work out the arrangements.

Dixon also said he is confident that the president "respects the strength of the system, with the checks and balances" built into the division of power among executive, legislative and judicial branches of government.

Although he still has not visited the White House as chairman of the Council, Dixon plans to make it some day soon.

"When I go," Dixon said, "it will be the right time."

"We're not trying to exclude anyone," a White House aide said yesterday. "We hope to have Arrington here for lunch some day soon."