WASHINGTON — Defying requests from the White House, four senators are making a pilgrimage to Damascus.

They say they want to test the Syrian regime’s intentions, but critics charge they are coming close to pursuing a private foreign policy.

Senator Bill Nelson, a Democrat from Florida, met yesterday with President al-Assad. The Democratic presidential nominee in 2004, Senator Kerry of Massachusetts, will be visiting Mr. Assad in the coming days. Also slated to travel to Syria for meetings with Mr. Assad are Senator Specter, a Republican from Pennsylvania who attended Hafez al-Assad’s funeral in 2000, and Senator Dodd, a Democrat from Connecticut, who was urged by Foggy Bottom not to follow through on his plans to visit the Syrian leader during a trip to the region in April.

The diplomacy from the lawmakers represents a challenge to the Bush administration, which is now weighing advice from the bipartisan Iraq Study Group to engage Syria and Iran in an effort to corral the regimes into helping stem the violence in Iraq. The study group also recommended that America pursue a peace deal between Syria and Israel that involves Israel ceding the Golan Heights to Syria.

Mr. Bush has indicated that he would be willing to talk only to the Syrian regime, which he has accused of harboring terrorists sabotaging Iraq, if it showed an interest in making peace. Yesterday he repeated that he took the recommendations from the bipartisan study group “seriously,” but he also said, “I’ve heard some ideas that would lead to defeat, and I reject those ideas — ideas such as leaving before the job is done; ideas such as not helping this government take the necessary and hard steps to be able to do its job.”

When asked about the upcoming trips by the senators to Syria, the White House spokesman, Tony Snow, said, “We don’t think that members of Congress ought to be going there.” Nonetheless, America’s embassy in Damascus will be assisting the lawmakers in the coming days. “Just because we offer those services and offer that assistance doesn’t mean we think it’s a good idea,” a State Department spokesman, Sean McCormack, said.

When asked to elaborate on why he thought the trips were not a good idea, Mr. McCormack said, “Our view is that the Syrian government knows fully well what it needs to do and certainly the United States is not going to pay the price for mere engagement with Syria in trading on the freedom of the people of Lebanon or looking the other way on the U.N. tribunal investigating the murder of former Prime Minister Hariri.”

This message was emphasized yesterday by the White House, which released a presidential statement urging the Syrian regime to free five political prisoners: Aref Dalila, Michel Kilo, Anwar al-Bunni, Mahmoud Issa, and Kamal Labwani. In the statement, Mr. Bush said he was troubled the five prisoners were being held in jails with violent criminals and that America supports freedom and democracy for Syria.

Mr. Nelson yesterday reported back that he was optimistic Syria’s stance on Iraq could be turned around. “Assad clearly indicated the willingness to cooperate with the Americans and or the Iraqi army to be part of a solution,” the Associated Press quoted the senator as saying.

Syria and Iraq opened embassies in their respective capitals this week. Over the weekend, Iraq’s former deputy prime minister, Ahmad Chalabi, held discussions with Syria’s foreign minister on a possible rapprochement with America.

Yesterday an aide to Mr. Kerry told the Sun that Mr. Kerry would be meeting with Mr. Assad in order to test his intentions on Iraq. “Syria is a very important country because they are a big part of the problem in Iraq, Lebanon and the Palestinian territories now,” she said. “But by the same token, they have the potential to be a part of the solution if they will change course.”

This aide also cited the recommendation to engage Syria from the Iraq study group chaired by a former Secretary of State, James Baker, and a former chairman of the House International Relations Committee, Lee Hamilton. That report was also cited by a spokesman for the incoming Senate majority leader, Harry Reid, a Democrat of Nevada. “The Baker Hamilton report called for increased dialogue with some of these countries,” the Reid spokesman, James Manley, said. “The administration thinks that it’s a sign of weakness to talk to our enemies. The fact is it’s a sign of strength to talk to our enemies.”

Not all Democrats agree, however. A former spokesman for President Clinton’s national security council, P.J. Crowley, said the timing of the visits were “dangerous.”

“The fact that senators are going even as the president and his administration continue to evaluate the recommendations of Baker Hamilton, what that means on direct discussions with Syria, well it’s risky. It risks sending a mixed message to the Syrians, if for example the senators hold out hope for one course of actions and the president chooses a different course of action.” Mr. Crowley said that he personally favored trying engagement with Syria, but that it was “always best when the United States government is speaking consistently with a clear message.”

The executive vice chairman of the Conference of Major American Jewish Organizations, Malcolm Hoenlein, yesterday came close to calling the lawmakers naïve. “I understand the intent of those going to see him in the hope of convincing him to change his policies, or at least to see of there is some prospect of change. But Assad is no longer an independent decision maker because he has become a puppet of Ahmadinejad and secondly his stated interests, supported by Assad’s actions, are inimical to America’s interest and stability in the region.”