"We are determined to assure the safety of the hostage," Jubeir said to CNN, but "we don't negotiate with terrorists. We don't negotiate with hostage-takers."
The United States also applies a non-negotiation policy with terrorists said Kelly Shannon, spokeswoman for the U.S. State Department's Bureau of Consulate Affairs.
"We do not make concessions to terrorists," Shannon told United Press International.
Johnson's family back home are living tense hours as Saudi officials began searching for Johnson, a difficult task, agreed experts on hostage situations. The FBI said they were ready to offer any assistance to the Saudis, should it be requested.
Johnson was abducted June 12 in Riyadh, the Saudi capital. The 49 year-old Lockheed Martin engineer was shown on an Islamist website Wednesday, as a man identified as al-Qaida's leader in the kingdom demanded the release of prisoners. He also requested that all Westerners leave the country, failing which, the blindfolded New Jersey native would be killed in 72 hours.
With the deadline approaching, Georgetown University Government and Foreign Service Professor Anthony Clark Arend said the United States will continue its policy of not negotiating with terrorists.
"The logic is that as soon as you open the door to these types of negotiations, you encourage more hostage-taking," Arend said.
The State Department Counter-Terrorism Office website states that "it is U.S. government policy to deny hostage takers the benefits of ransom, prisoner releases, policy changes, or other acts of concession" while using "every appropriate resource to gain the safe return of American citizens who are held hostage."
However, this policy has not always been adhered to. One example is the 1980s Iran-Contra affair that occurred during Ronald Reagan's presidency, when arms were secretly sold to Iran in an attempt release American hostages held in Lebanon by pro-Iranian groups.
Arend, the Georgetown professor, expressed concern about the rising violence aimed at Westerners in the Middle East. The kidnapping and murder of Nicolas Berg in Iraq last May; the killing of four civilian security contractors in Fallujah in March and the recent deaths of three Westerns, killed in a single week in Saudi Arabia, are all "extremely troubling."
"They (the terrorist) are trying to drive U.S. nationals out of Iraq and Saudi Arabia with fear," said Arend. "Terrorist acts seem to be increasing as we near the date of sovereignty for Iraq."
Harlan Ullman, senior adviser with the Center for Strategic and International Studies in Washington, highlighted the difficult nature of the hostage situation set on the backdrop of the war in Iraq.
"There are complications, in terms of a lack of a formal situation (in Iraq)," said Ullman. "The question really is who seized him and who is in charge."
The U.S. State Department will not release the number of Americans currently living in Saudi for safety reasons, but has encouraged all United States citizens to leave the country. Some have already departed, said a State Department spokeswoman.
Johnson's son, Paul Johnson III, appeared with family members on television. "I respect your country, I respect everything that everybody has done and I just want my father brought home safely," he said. Speaking to the Saudis, he said, "You can make it happen and I'm just asking you please make it happen."