LONDON — President Bush is sending his national security adviser to the Middle East next week to keep up pressure on Israel and the Palestinian Arabs to reach agreement on launching formal peace talks, a senior American official said today.

The announcement came as Secretary of State Rice said she was encouraged by what she had heard from the two sides during four days of intense talks with Israeli and Palestinian Arab officials and civic and business leaders in Jerusalem and Ramallah in the West Bank.

But Ms. Rice also acknowledged tensions between the two sides as they try to craft a joint statement that will be presented at an American-hosted conference in late November or December at Annapolis, Md., where America hopes to announce the start of new formal peace negotiations to create a Palestinian Arab state.

“I think they are very serious,” Ms. Rice told reporters today as she flew to London for talks with Jordan’s King Abdullah. “The teams are serious. The people are serious. The issues are serious. So I am not surprised that there are tensions. I am not surprised that there are some ups and downs.

“That is the character of this kind of endeavor, but I was encouraged by what I heard,” she added.

National Security Adviser Stephen Hadley will visit the Middle East next week to follow up on Ms. Rice’s current round of diplomacy and Ms. Rice will return to the region for further discussions with Israelis and Palestinian Arabs at the end of the month or in early November, the American official said.

The trip will also take Ms. Rice to an Iraq neighbors meeting in Istanbul, Turkey, said the official, who spoke on condition of anonymity because neither the Hadley trip nor Ms. Rice’s return visit have been formally announced. The official did not give specific dates for the travel.

Mr. Hadley and Ms. Rice will press Israel and the Palestinian Arabs to bridge significant gaps on the substance of the conference’s joint declaration, which would outline a way for the two sides to return to the negotiating table after seven years of bloodshed and diplomatic paralysis.

The Palestinian Arabs and their Arab allies such as Egypt and Jordan are insisting the document be detailed and specific with a timetable for formal peace talks, and the Israelis want language that is more vague.