President Carter's national security adviser. Zbigniew Brzezinski, said yesterday that the United States has a "direct interest" in the outcome of the Middle East conflict and therefore "has a legitimate right to exercise its own leverage" to obtain a settlement.

"And that's exactly what we will be doing," Brzezinski said in an interview with Canadian Television Network Ltd.

Brzezinski's unusually sharp statement seemed to indicate a growing determination within the Carter administration to push for the reconventing of the Geneva Middle East peace conference within the framework of the Soviet-American declaration on joint objectives for a peace settlement issued Saturday in New York.

Israel has already described the joint declaration as "unacceptable."

The interview was taped here Saturday before the declaration was made public, but Brzezinski suggested that the administration had reached an agreement with the Soviets.

"The Soviet Union, too, realizes that the situation of continued conflict (in the Middle East) does not enhance its interests. It jeopardizes them locally and in terms of their relations with us," he said, according to a transcript of the interview.

"I am reasonably hopeful that before the end of this year we, in fact, will be having a conference in Geneva," he added.

Asked what made him believe that the Israelis would agree to attend, Brzezinski said. "I don't think they want to be left alone, out of the process which has a settlement as its ultimate objective; and therefore, they will be there."

"I think the point to bear in mind is that the United States is not just an interested bystander, not even just a benevolent mediator," he said later.

"The United States has a direct interest in the outcome of the Middle Eastern conflict. The United States has a direct interest in obtaining a resolution of the conflict. And therefore the United States has a legitimate right to exercize its own leverage, peaceful and constructive, to obtain a settlement. And that's exactly what we will be doing."

Brzezinski expressed optimism about a prospective settlement, saying all parties to the conflict "have realized that they need peace." He said that the continued beligerency would lead to a stagnation of Israel's economy while her Arab neighbors would become more radical and more modern.

He said Israeli Prime Minister Manahem Begin is "one of the very few people who . . . has had the opportunity to fight for a cause and to see it prevail.

"And now he (Begin) has the last chance opportunity of his life to give his people lasting peace. I don't think when he is faced with that opportunity in the final analysis that he will shrink from seizing it."