WASHINGTON — The State Department is reaffirming its official commitment to avoid negotiating with Hamas after the disclosure over the weekend that a senior adviser to the American general in charge of training a Palestinian Authority security force had visited Gaza twice to meet with the Iranian-backed terrorist group.

Over the weekend, Agence France Presse disclosed that a senior aide to General Keith Dayton had met with Hamas officials in Gaza on two separate occasions. The New York Sun has since learned from Israeli and American sources that the individual in the meetings was Michael Pirson, a Canadian colonel who also serves as defense attaché for Canada’s embassy in Tel Aviv.

Details of his mission remain murky. One Israeli official said Mr. Pirson was visiting Gaza on official Canadian business.

A State Department official who requested anonymity said, “Nobody at the direction of the Americans is meeting with Hamas.” This official went on: “The rules for the Americans are extremely tight. General Dayton is responsible for security reforms including training the presidential guard and other Palestinian security services.”

Mr. Dayton’s mission, in effect, is to prepare forces loyal to Palestinian president, Mahmoud Abbas, for clashes with Hamas gun men. In June, Hamas guerrillas bested Mr. Abbas’s Fatah-affiliated preventive security forces in Gaza, ousting them from the security headquarters built for them in the 1990s with American money. As a result of the battle in Gaza, Hamas now enjoys political control of that territory, which was vacated by Israel in 2005. General Dayton testified on the preparedness of the Fatah troops to Congress only a week before they were beaten in Gaza.

On Monday, ahead of President Bush’s scheduled visit to Israel, Egypt’s national security adviser, Omar Suleiman, is scheduled to deliver a cease-fire offer from Hamas. That offer follows weeks of Israeli operations in Gaza in retaliation for the daily barrages of Qassam rocket attacks from Gaza on Israel.

A spokesman for Prime Minster Olmert told the Israeli press that the Jewish state would welcome a cease-fire from Hamas. The spokesman, Aryeh Mekel, said, “The ball is in Hamas’s court. If they were to stop these attacks, Israel will have no reason to react and there will be peace and quiet,” according to the Voice of America.

Israel negotiates through Mr. Suleiman’s offices indirectly with Hamas, but those talks are limited to a possible prisoner exchange aimed at the return of Gilad Shalit, who was abducted by Palestinian Arab kidnappers in 2006.

Since the Hamas victory in Gaza, America has attempted to isolate the group diplomatically and encouraged negotiations between the government of Israel and Mr. Abbas’s West Bank regime toward the creation of an independent Palestinian State.

President Bush is scheduled to arrive in Jerusalem this week for talks with the Israeli government as part of a regional tour. The White House last week said he would not seek a meeting with both Prime Minister Olmert and President Abbas together, a sign that negotiations between the two leaders have yielded little progress.

Last week, Secretary of State Rice privately told both leaders that they risked an erosion of public support for the peace process if they failed to reach any interim agreements, according to the Associated Press.