President Reagan and several senior administration officials talked about domestic politics and Middle East diplomacy yesterday with members of the newly founded Arab American Institute, which is seeking to increase participation of Arab Americans in national and local U.S. elections.

Reagan told eight leaders of the group in an Oval Office meeting that he appreciated Arab Americans' support in his reelection campaign and "encouraged us in a bipartisan way" to get more involved in politics, according to James Zogby, former executive director of the American-Arab Anti-Discrimination Committee.

Later, 160 conference participants were given briefings on Middle East diplomacy by Assistant Secretary of State Richard W. Murphy and on domestic policy by White House adviser John A. Svahn, said Zogby.

The meetings were closed to reporters. The White House did not list the meeting on the president's public schedule. However, a spokesman announced at a daily White House briefing that Reagan would be photographed with some members of the group.

Reagan told the smaller group that he is optimistic about recent developments in the Middle East, Zogby said, but did not mention the recent diplomatic exchanges involving Jordan, the Palestine Liberation Organization and Egypt.

Zogby said Reagan expressed his "real concern" for the "plight of the people in South Lebanon," and he quoted the president as saying "legitimate rights for Palestinians have to be met."

On the question of the United States talking to the PLO, Reagan said the stumbling block continues to be PLO refusal to accept United Nations Resolution 242. The resolution called for Israeli withdrawal from territories gained in the 1967 war in return for peace in the region, secure borders for all nations and a "just settlement" of the Palestinian "refugee problem."

Zogby said there was a "difference of opinion" with the administration over its approach to the PLO. He said members of the group would like the United States to open "a dialogue" with the PLO despite a U.S. pledge not to negotiate with the PLO until it accepts the U.N. resolution.

Those who met with Reagan included Zogby, a vice chairman of Jesse L. Jackson's 1984 presidential campaign; Salem, a Washington attorney and former executive director of the ethnic voters division of the Reagan-Bush Committee; Samir Totah, a representative of the American Ramallah Federation, the largest Palestinian-American organization; David Saad, of the National Association of Arab Americans; Omar Kater, of the American-Arab Anti-Discrimination Committee; Casey Kasem, a broadcast personality who is an American of Druze descent; Susan Syadeh, of the Association of Arab American University Graduates; and John Zogby, one of the directors, along with James Zogby and Salem, of the new institute.