America's strategic relationship with Saudi Arabia may permanently change if Riyadh does not end its latest oil price war, Sen. Dan Sullivan told CNBC on Wednesday.

"The Saudis have really brought in a supply shock at exactly the wrong time," the Alaska Republican said on "Squawk Box." "These kind of crises really make it clear … who your friends are and who aren't your friends."

Sullivan said that a group of U.S. senators has been applying pressure on Saudi Arabia, writing a letter to Crown Prince Mohammed bin Salman that was followed up by call with the Saudi ambassador to the U.S. in Washington.

"All of the senators who were on that letter, on that conference call with the ambassador, have been strong supporters of the U.S.-Saudi relationship," said Sullivan. "That is going to change if the Saudis don't start playing a more constructive role with regard to energy markets."

Sullivan, who represents the oil-rich state of Alaska, said he reminded the Saudi ambassador of the past U.S. defense of the kingdom.

"We've been there for you," Sullivan said he told her. "First Gulf War, Saddam Hussein is getting ready to roll through your country. It wasn't the Saudi military that stopped him. ... It was the First Marine Division, 82nd Airborne. Americans died in that war."

The Saudi Embassy was not immediately available to respond to CNBC's request for comment.

"They need to step up or the strategic relationship is going to change," added Sullivan, also a colonel in the U.S. Marine Corps Reserve.

Oil prices have fallen sharply since early March, pushed down by a two-sided shock from the coronavirus pandemic and global producer infighting.

Earlier this month, Saudi Arabia announced plans to increase production after an output cut deal among the so-called OPEC+ nations fell apart. Russia led the opposition to the reduction in output.

Declining oil prices have made it unprofitable for many U.S. firms to remain active, analysts have said.

"The Saudis are hoping to drive out of business American producers, and in particular shale producers, largely in the Permian Basin in Texas and in North Dakota," Republican Sen. Ted Cruz told CNBC on Monday. He represents the leading oil producing state of Texas.

Cruz, who also was on the phone call with the Saudi ambassador, added, "That behavior is wrong, and I think it is taking advantage of a country that is a friend."