President Reagan yesterday told Israeli President Yitzhak Navon that the United States intends to pursue its controversial Mideast peace initiative, and Navon replied that, despite opposition to the plan in his country, all Israelis believe that Reagan is dedicated to their security.

Following a meeting and luncheon at the White House, Navon told Reagan: "In Israel, though there are different views as to policies--whether of those who accepted the American views as a basis for negotiations or whether of those who didn't find it possible--none of them has any doubt as to your dedication to peace, your sincerity and your commitment to the security of Israel."

Navon's visit, which had been postponed twice, comes at a delicate time for the administration. The situation is being watched closely in Israel for signs of whether Reagan, confronted by Israeli Prime Minister Menachem Begin's rejection of his initiative, might be encouraging Navon to challenge Begin politically.

Navon, whose duties as president are largely ceremonial, comes from the opposition Labor Party, whose leadership has been more receptive to the Reagan initiative's call for Israel to grant the occupied West Bank and Gaza Strip eventual independence "in association with Jordan."

Navon must decide next month whether to seek another five-year term as president or return to partisan politics. He has been mentioned widely as a potential compromise candidate who might be able to heal a split in the Labor Party leadership and challenge Begin for prime minister in Israel's next national elections.

Because of that situation, the White House has gone to great lengths to stress that Navon came here solely in his position as Israel's head of state and that the administration has no intention of intervening in internal Israeli politics.

That point was underscored repeatedly by a senior administration official who briefed reporters following yesterday's meeting. The official, who declined to be identified, said there had been no discussion of Israel's political situation or controversial aspects of U.S.-Israeli relations.

Similarly, the official continued, Navon made clear that he was here in a bipartisan role and confined himself to subjects that he regards as issues on which there is a consensus within Israel.

In particular, the official said, Navon told Reagan that all Israelis are concerned that, in any peace solution, there should be no division of Jerusalem and no creation of an independent Palestinian state in the occupied territories.

Reagan, the official noted, reaffirmed his commitment to Israel's security, his determination to keep pushing his peace initiative and his hopes for a quick withdrawal of Israeli and other foreign forces from Lebanon. But, the official stressed, "It was not a session where issues of substance were being negotiated."

Despite the speculation in the Israeli and American press, U.S. officials privately have insisted that Navon's visit is not seen here as having major impact on the administration's efforts to advance the Reagan initiative.

Instead, the officials said, the next important steps for the peace process are likely to begin unfolding next month. At that time, Begin is expected to come here in an effort to persuade Reagan to drop the U.S. proposals; and Jordan's King Hussein, who conferred with Reagan before Christmas, could return with a decision on whether he is willing to join broadened peace talks.

Also during February, the independent Israeli commission investigating whether Begin or members of his government bear any responsibility for the September massacre of Palestinian civilians in Beirut is expected to announce its findings.

That, coupled with anticipated decisions by Navon and other Israeli political leaders as to whether they intend to challenge Begin, will have potentially profound effects on Israel's internal political situation and, by extension, on Israel's future approach to the peace process.